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1 MAXIMIZING THE USE OF MOLECULAR MARKERS IN PINE BREEDING IN THE CONTEXT OF GENOMIC SELECTION By PATRICIO R. MUNOZ DEL VALLE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLME NT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2012
2 2012 Patricio Munoz Del Valle
3 To my wife for all he r support in this long and rough road
4 ACKNOWLEDGMENTS I would like to thank my committee for a ll their support in these years Special thanks to Dr. Gary Peter because he always supports me and found the time in his busy agend a to discuss important topics of my research as well as b roader areas. Thanks to Dr. Matias K irst for his support, time and constant push toward a better science. Thanks to Dr. Joh n Davis for helping me improve considerably my understanding on genetics of plant diseases Thanks to Dr. James Olmstead for his support and for give me a chance to interact with students from the oth er side of the classroom T hanks t o Dr. George Casella, who originally was in my committee, he helps me understanding the number and formulas when they were too entangled for me I have long conversation and discussion of several imp ortant and daily trivia l topics with all of you that in different ways help me to improve my holis tic view of research and science. I would like to thank my family, especially to my wife (Claudia), my daughter (Antonia) and son (Ignacio) for their love, support in all times, und erstand me in difficult times and for disconnecting me from demanding research. Thanks to my parent, brother and sisters, for their love and for helping me to reach my goals from the beginning. Thanks to my friends and colleagues e specially Thomas and Cha rlotte for their support and friendship that I am sure will last until the end of our days. Thanks to Dr. Salvador Gezan and Marcio Resende for their friendship, constant support, great discussions and helping me increase my knowledge in different areas of programming, statistics and more. To the Chilean community ( families: Gonzalez Costagliola, Riveros Chavez, Garcia Villaseor Forcael Salgado, Rodriguez Hananias and Gladys, Andres, Francisco, Fernando Rodrigo ) for their friendship and support. T hanks t o my
5 colleagues Greg Powell Eliana Kampf and Chris Dervinis, for their constant support and their important role on logistics in their respective areas. Finally, I would like to thanks to all the members of the Forest Genomic Lab, the Plant Molecular and Cellular Biology program ( PMCB ) the Plant Molecular Breeding Initiative ( PMBI ) the Cooperative of Forest Genetic Research Program ( CFGRP ) and the Forest Biology Research Cooperative ( FBRC ) for their support in different aspect of my research
6 TABLE OF C ONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 8 LIST OF FIGURES ................................ ................................ ................................ .......... 9 LIST OF ABBREVIATIONS ................................ ................................ ........................... 10 ABSTRACT ................................ ................................ ................................ ................... 11 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 13 2 DENSE PANEL OF MARKERS FOR CORRECTING PEDIGREE ERRORS IN BREEDING POPULATIONS: IMPACT ON HERITABILITY, BREEDING VALUE AND GENOMIC SELECTION ACCURACY ................................ ............................ 19 Bac kground ................................ ................................ ................................ ............. 19 Methods ................................ ................................ ................................ .................. 21 Data ................................ ................................ ................................ .................. 21 Realized Relationship Matrix and P edigree Corrections ................................ .. 22 BLUP/REML Analysis: Variance Component Estimation and Breeding Values Prediction ................................ ................................ .......................... 23 Original pedigree BLU P (Ori BLUP) ................................ ........................... 23 Corrected pedigree BLUP (Corr BLUP) ................................ ..................... 24 Genomic Selection and Validation ................................ ................................ .... 24 Results ................................ ................................ ................................ .................... 25 Pedigree Correction ................................ ................................ ......................... 25 Estimation of Breeding Values with Original and Corrected Pedigree Relationship Matrices ................................ ................................ .................... 26 Accuracy of Genomic Selection Predictive Models with Original and Corrected Pedigrees ................................ ................................ ..................... 26 Discussion ................................ ................................ ................................ .............. 27 Pedigree Correction ................................ ................................ ......................... 27 Estimation of Breeding Value with Original and Corrected Relationship Matrices ................................ ................................ ................................ ......... 29 Accuracy of Genomic Selection Predictive Models with Original and Corrected Pedigrees ................................ ................................ ..................... 30 3 ACCURACY OF GENOMIC SELECTION METHODS IN A STANDARD DATA SET OF LOBLOLLY PINE ( PINUS TAEDA L.) ................................ ....................... 35 Background ................................ ................................ ................................ ............. 35 Materials and methods ................................ ................................ ............................ 37
7 Training Population and Genotypic Data ................................ .......................... 37 Phenotypic Data ................................ ................................ ............................... 37 Breeding Value Prediction ................................ ................................ ................ 38 Statistical Methods ................................ ................................ ........................... 39 Random Regression Best Linear Unbiased Predictor (RR BLUP) ............. 40 Baye s A ................................ ................................ ................................ ...... 41 ................................ ................................ ................................ ... 41 Bayesian LASSO ................................ ................................ ....................... 42 RR BLUP B ................................ ................................ ................................ 42 Validation of the mod els ................................ ................................ ............. 43 Accuracy of the models ................................ ................................ .............. 44 Results ................................ ................................ ................................ .................... 45 Cross Validation Met hod ................................ ................................ .................. 45 Predictive Ability of the Methods ................................ ................................ ...... 45 Bias of the Methods ................................ ................................ .......................... 46 Markers Subset and RR BLUP B ................................ ................................ ..... 46 Discussion ................................ ................................ ................................ .............. 48 4 THE RE DISCOVERY OF NON ADDITIVE EFFECTS WITH GENOMIC RELATIONSHIP MATRICES A ND ITS IMPLICATION IN BREEDING ................... 54 Background ................................ ................................ ................................ ............. 54 Materials and Methods ................................ ................................ ............................ 57 Data ................................ ................................ ................................ .................. 57 Relationship Matrices ................................ ................................ ....................... 57 Genetic Analyses ................................ ................................ ............................. 58 Te sting and Validation of Models ................................ ................................ ..... 61 Results ................................ ................................ ................................ .................... 61 Discussion ................................ ................................ ................................ .............. 65 5 CON CLUSIONS ................................ ................................ ................................ ..... 75 APPENDIX A PREDICTIVE ABILITY, STANDARD ERRORS AND REGRESSION COEFFICIENTS FOR DIFFERENT GENOMIC SELECTION MODELS OF CHAPTER 2 ................................ ................................ ................................ ............ 80 B SAMPLING CORRELATION MATRICES FOR CHAPTER 4 MODELS ................. 86 LIST OF REFERENCES ................................ ................................ ............................... 88 BIOGRAPHICAL SKETCH ................................ ................................ ............................ 95
8 LIST OF TABLES Table page 2 1 Age of trait measurement and code trait age combination ................................ 31 2 2 Ori ginal and corrected pedigree mean and standard deviation for relationship classes in the population. ................................ ................................ ................... 31 2 3 Number of individuals in each pedigree category in the original and new pedigree ................................ ................................ ................................ ............. 31 2 4 Narrow sense heritability accuracy of breeding values and fitting of models by traditional BLUP analysis using a full genetic model with original pedigree or using a full genetic model w ith corrected p edigree on 15 trait age combination. ................................ ................................ ................................ ....... 32 3 1 Predictive ability of Genomic Selection models using four different methods .... 50 4 1 Summary of models, effects fitted and relationship matrices used in the study. ................................ ................................ ................................ .................. 70 4 2 Variance estimation, genetic parameters and measure of data fitting. ............... 71 4 3 Predictive ability, Mean Square Error top 10% rank ing correlation and AIC for selected models. ................................ ................................ ........................... 72 A 1 Predictive ability and standard error of RR BLUP model under two different cross validation methods: 10 fold cross validation and leave one out ............... 80 A 2 Regress ion Beta and standard error of the RR BLUP model with two different cross validation methods: 10 fold cro ss validation and leave one out ................ 81 A 3 Standard error of the prediction models for the different methods tested. .......... 82 A 4 Accuracies of genomic selection models in 17 different traits of loblolly pine.. ... 83 A 5 Regression coefficients estimates of deregressed phenotypes reg ressed on Direct Genetic Values ................................ ................................ ........................ 84 B 1 Sampling correlation matrix for all models tested. ................................ .............. 86
9 LIST OF FIGURES Figure page 2 1 Distribution of relationship values for half sib and full sib individuals around their expected means 0.25 and 0.5, respectively.. ................................ .............. 33 2 2 Predictive ability for fiftee n different traits using the original pedigree derived from historical records (White column) and the corrected version of the pedigree (Grey column). ................................ ................................ ..................... 34 3 1 Regression of RR BLUP predictive a bility on narrow sense heritability for 17 traits (trend line is shown, R 2 =0.79) ................................ ................................ .... 51 3 2 Example of the two patterns of predictive ability observed among traits, as an increasing number of mark ers is added to the model. a) For DBH. b) For the trait Rust_gall_vol. ................................ ................................ .............................. 52 3 3 Predictive ability for subsets of 310 markers for Rust_bin, 110 markers for Rust_gall_vol and 240 markers for Dens ity. ................................ ....................... 53 4 1 Eigenvalues distribution for a perfect orthogonal correlation matrix (a), for models including additive and dominance (b) and for models including additive, dominance and epistasis (c).. ................................ ............................... 73 4 2 Standa rd error of the prediction for pedigree derived matrices model against their counterpart using markers derived matrices ................................ .............. 74
10 LIST OF ABBREV IATIONS AIC Akaike information criteria BA Average branch angle BD Average branch diameter BLC Basal height of the live crown BLUP BV Traditional best linear unbiased predicted breeding value BV Breeding values CWAC Crown width across the planti ng beds CWAL Crown width along the planting beds DBH Stem diameter at chest height GS Genomic Selection GS BV Genomic selection predicted breeding value HT Total stem height RRM Realized relationship matrix SNP Single nucleotide polymorphis m SSR Simp le sequence repeat
11 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy MAXIMIZING THE USE OF MOLECULAR MARKE RS IN PINE BREEDING IN THE CONTEXT OF GENOMIC SELECTION By Patricio Munoz Del Valle December 2012 Chair: Gary F. Peter Major: Plant Molecular and Cellular Biology By 2030 demand for renewable energy, food and fiber is expected to double. To sustainably meet this increase in demand from the current land base p lant breeders need to develop higher yielding crops that require fewer inputs and better resist diseases and environmental change. Of particular importance is accelerating improvement in quantitati ve traits (QT), which show complex patterns of inheritance. Genomic selection (GS) provides an approach where molecular markers can be used directly in breeding programs regardless of the genetic architecture. While most GS studies have concentrated on pre diction of breeding values, here this approach is extended to include non additive variation and to maximize the use of molecular markers (SNPs) in pine breeding. With a relatively dense panel of SNPs, a method to detect and correct errors in the pedigree information is presented, based on a marker derived additive relationship matrix. The impact of pedigree errors on genetic parameter estimates and breeding value prediction is demonstrated. In addition, the performance of four published analytical methods for GS that differ in assumptions regarding the distribution of markers additive effect is presented. Methods include: ridge regression best linear
12 unbiased prediction (RR BLUP), Bayes A, Bayes C p i and Bayesian LASSO. Furthermore, a modified RR BLUP (RR B LUP_B) that utilizes a selected subset of markers was developed and evaluated. All five methods for GS were evaluated for seventeen different traits of importance in pine breeding and with different predicted genetic architecture and heritabilities. While for QT no significant difference among methods was detected, for traits controlled by fewer genes, Bayes Cpi and RR BLUP_B performed significantly better. Finally, t he use of a dense panel of SNPs to partition the genetic variance into additive and non add itive components was evaluated. For tree height use of the SNP derived relationship matrices (additive and non additive) in a statistical model including additive and non additive effects performed best, not only to partition the genetic variances but als o to improve considerably the breeding value prediction ability in trend, magnitude and top individual selection This study indicates that markers can be used beyond prediction of additive effects, positively impacting the genetic gain of the breeding pro gram.
13 CHAPTER 1 INTRODUCTION Our rapidly expanding population and their desire for a better standard of living are quickly increasing demand for renewable energy, food and fiber (FAO 2002). At the same time, less land is available for production due to i ncreased urbanization, climate variability and environmental change (IPCC 2007). To meet these increases in demand, with less land, plant breeders need to accelerate development of higher yielding crops that require fewer inputs and better resist diseases and environmental change (Collard and Mackill 2008 ). To help meet these challenges molecular markers offered the promise of accelerating genetic improvement ( Stuber et al. 1982, Soller 1978 ). Unfortunately marker assisted selection (MAS) only worked in a few cases where traits were controlled by a small number of genes (Lande and Thompsom 1990; Dekkers 2004; Jannink et al. 2010). However, most economically important traits in animal and plant breeding programs show complex inheritance and are quantitative traits (Buckler et al. 2009; Goddard 2009c; Hayes and Goddard 2010). Quantitative traits are controlled by a large number of genes, each with a small effect only detectable using large population s (Visscher 2008). For quantitative traits selecting for pos itive alleles in a few of the hundreds of genes affecting a trait has limited applicability in breeding (Bernardo 2008). To overcome this limitation, a new methodology known as genomic selection (GS) was proposed. GS uses all molecular markers simultaneous ly (as a random effect) to make predictions in the breeding context (Meuwissen et al. 2001). In GS, breeding values (BV) obtained from traditional Best Linear Unbiased Prediction (BLUP BV) analysis of phenotypic data from a training population are used to develop GS prediction models based on genotypic (molecular
14 markers) information. GS models predict the genomic BVs (GS BV) for a validation population, which are then correlated with known traditional BLUP BVs to estimate the accuracy of the models (Goddar d and Hayes 2009) The overall idea of GS is to select genotypes in advanced generations based only on the GS BV predicted from the molecular marker information using models previously constructed and validated with the parental population (Hayes and Godda rd 2010). From the statistical point of view, GS has advantages over other methods (e.g. least square means), because it accounts for the co linearity of molecular markers since all co variables (markers) come from the same individual. Also, in GS all mark ers are retained for prediction, enabling the capture of more variation due to small effect quantitative trait loci (QTL), and un detected causal loci (Hamblin et al. 2011). GS c an be used for any trait independent of its genetic architecture thus predict ions using GS can be performed for quantitative traits while MAS is limited to traits with few genes of large effe ct (Jannink et al. 2010). From the point of view of breeding, GS provides higher accuracy for prediction and shorter rotations than current ph enotypic selection, which translates into increased genetic gain per unit time (Resende et al. 2012a). The greatest theoretical and practical advances in GS have occurred with cattle breeding (Hayes 2009b) aimed at decreasing the cost of testing that can reach as much as $50,000 per bull (Schaeffer 2006). Bulls are selected by their additive genetic value (General combining ability, GCA), ignoring non additive effects. In this respect, GS methods and models developed for cattle are completely equivalent to traditional animal breeding as they both only consider additive effects. Consequently, commercial dairy cattle breeding programs currently use additive GS models operationally (Wiggans et al.
15 2011). However, plant breeding programs differ substantially fr om cattl e breeding. Plant breeder s use mating designs with complex pedigrees, and often exploit non additive effects through full sib families or cloning of progeny for deployment (White et al. 2007). In the case of conifers breeding is a long, complex mu lti step process (White and Carson 2004) three cycles of breeding and selection have been completed with the most advanced programs only in the ir fourth cycle of improvement (Neale and Kremer 2011). During this time, a number of advances have been made to accelerate pine breeding and improve genetic gain, the most important being the use of top grafting of immature scion into sexually mature trees (Bramlett 1997), and early selection for growth traits (Lambeth 1980). Even with th ese improvements pine breeding and selection cycles still span more than a decade. Thus, i n tree breeding the general objective of implementing GS is to shorten the breeding cycle th ereby inc reasing the gain per unit time. Recently the potential for dram atic increases in genetic gain per cycle with GS have been shown (Wong and Bernardo 2008; Iwata et al. 2011; Resende et al 2012a) considering only additive effects T he reality is that tree breeders exploit additive as well as non additive effects (White el at. 2007). A single parent can be crossed to several other individuals (as male and female) full sib progeny from these crosses are tested as seedlings and/or clonally propagated cuttings, and families are then selected by their deviation relative to t he average of the two parents (Specific Combining Ability). In addition, these crosses are performed under mating designs that create complex relationships (pedigrees) in a few generations of improvement (White and Carson 2004).
16 Given the important differ ences between tree and cattle breeding, development of GS models that are completely equivalent to traditional tree impro vement scenarios are a priority. Additionally, considering the potential for success of GS in plant breeding and the rapidly decreasing cost of molecular markers, especially single nucleotide polymorphism (SNP), the use of molecular markers and GS likely will soon become the norm in all breeding programs. This implies an important initial investment to obtain SNP markers in a significant number of individuals (Collar d and Mackill 2008 ). Although molecular markers (SNPs) as presented above are used exclusively for prediction of BV, they could be used in other beneficial ways for the breeding program. The objective of this research is to pr esent how to maximize the use of the molecular marker in pine breeding programs by pedigree corrections, GS analytic method selection and by exploring the trait genetic architecture. The length of the pine breeding cycle not only slows progress but also in creases the chance for errors because numerous people are involved in the many steps that need to occur over the 12 15 years it takes to complete one breeding cycle. Errors in the population pedigree decrease the accuracy of genetic prediction s which redu ces the genetic gains that can be achieved even with traditional phenotypic selection (Ericsson 1999; Banos et al. 2001; Sanders et al. 2006). Recently we concluded that the breeding cycle could be shortened by using GS with additive effects (Resende et a l. 2012a); however, errors in the pedigree will still reduce accuracies. I f molecular markers are developed with the purpose of using genomic selection for additive effects, then it should be possible to use them to first correct the pedigree to obtain les s biased BV and GS BV predictions Thus, the second chapter provides a method to detect and correct
17 errors in the pedigree information using a dense panel of markers that posteriorly will be used for GS. Although the pedigree can be corrected with a low de nsity of markers, such as microsatellites (SSRs), if GS is planned, then using the dense panel of markers needed for GS to first correct the pedigree will improve prediction model construction that in the practice will benefit the breeding program. Genomic selection is expected to be particularly valuable for traits that are costly to phenotype and expressed late in the life cycle of long lived species, such as pines (Resende et al. 2012a). Alternative approaches to genomic selection prediction models may p erform differently for traits with distinct genetic properties (de los Campos et al. 2009a; Habier et al. 2011; Meuwissen et al. 2001). In the third chapter the performance of four different original analytical methods of genomic selection: (i) ridge regre ssion best linear unbiased prediction (RR BLUP), (ii) Bayes A, (iii) Bayes C pi and (iv) Bayesian LASSO, that differ with respect to assumptions regarding distribution of marker effects, are evaluated and compared. In addition, a modified RR BLUP (RR BLUP B) that utilizes a selected subset of markers was evaluated. P roof of concept was provided in Resende et al. (2012a), which evaluate d GS for yield traits. This chapter extends the analysis to seventeen different traits of importance in pine breeding and wi th different predicted genetic architecture and heritabilities. The results show that correct selection of the methodology should be based on the genetic architecture of the trait. I n the Southeastern US, pine plantations exploit both additive and non addi tive effects as parental crosses are selected for family or clonal deployment (White et al. 2007). Incorporating non additive effects in GS has had less attention because it cannot
18 be exploited in cattle breeding where the most of the advances for GS have been made. Thus, for forest tree improvement it is important to explore how to incorporate non additive effects in the GS models, understanding the contribution to ge netic variance, and finally make GS fully comparable to the current methods of tree improv ement The fourth chapter uses a dense panel of molecular markers in a novel way to improve partitioning of the genetic variance into additive and non additive components. Unbiased estimation of the variance components is essential for breeding, as bias af fects BV prediction, which can be detrimental to the breeding program. Here we evaluated the potential of incorporating non additive effects into GS, which is highly relevant for tree breeding programs that typically exploit some portion of non additive ef fects by deployment of families or clonal material. In these cases, the use of GS with only additive effects does not fit with the necessities of the breeding program, by not exploiting non additive variation to improve genetic gain.
19 CHAPTER 2 DENSE PAN EL OF MARKERS FOR CORRECTING PEDIGREE ERRORS IN BREEDING POPULATIONS: IMPACT ON HERITABILITY, BREEDING VALUE AND GENOMIC SELECTION ACCURACY 1 Background A central goal of quantitative genetics is to estimate the level of genetic control and genetic correlat ion amongst complex traits. This information is used in breeding, for the selection of elite parents, families and individuals, as well as for subsequent generations of genetic improvement. Genetic tests are designed to provide phenotypic information for e stimation of parameters such as variance components, heritability, genetic correlations and breeding values. Breeding values (BV) are typically estimated with best linear unbiased prediction (BLUP BV), based on the theory of resemblance between relatives due to genetic factors ( Lynch and Walsh 1998 ) commonly derived from the pedigree ( Mrode 2005 ) Consequently, better estimates of genetic parameters are obtained when the pedigree information is accurate. P edigree errors are common averag ing 10% i n cattle and tree breeding populations ( Banos et al. 2001; Visscher et al. 2002; Doerksen and Herbinger 2010 ) The presence of such errors can lead to incorrect estimate s of the additive variance, caus ing a decrease in the BLUP BV prediction accuracy ( Erics son 199 9; Banos et al. 2001; Sanders et al. 2006 ) In traditional phenotypic selection, a decrease in BV accuracy has been shown to reduce genetic gain s by 4.3% to 17% ( Geldermann et al. 1986; Israel and Weller 2000 ) D ense panel s of molecular markers can be use d to empirically estimate the actual relationships between relatives through the construction of a realized relationship matrix ( R RM) ( Powell et al. 2010 ) and provide precise estimates of the proportion of the 1 Chapter submitted to Genomic Selection Evolution Journal
20 genome that is shared among individuals. Molec ular markers have been used to correct errors in the pedigree using different strategies; most of them rely on parent progeny genotype data ( Bennewitz et al. 2002; Wiggans et al. 2010; Hayes 2011 ) or in the diagonal of the RRM matrix ( Simeone et al. 2011 ) If a dense panel of markers is used in breeding populations with a complex pedigree, the R RM values among individuals are normally distributed around the expectation for a given class (i.e. expectation [ unrelated]=0.0) ( Yang et al. 2010; Simeone et al. 20 11 ) Thus, the current progeny population RRM diagonal and off diagonal elements can be used to correct pedigree errors. This corrected pedigree should increase the accuracy of the BLUP BV predictions. Increasing the accuracy of BLUP BV not only improves gains from traditional phenotypic selection, but should also improve the accuracy of genomic selection models. Genomic selection (GS) models are developed to predict BV using only information from esti mated marker effects ( Meuwissen et al. 2001 ) Typically the inputs for constructing GS prediction models are phenotypes deregressed from the BLUP BV ( Garrick et al. 2009 ) The models are then tested in a validation population to obtain GS predicted BVs (GS BV) and estimate the accuracy of genomic prediction ( Goddard et al. 2009 ) The u tility of GS in plant and animal breeding depends on the accuracy of the GS models developed to predict BV ( Goddard and Hayes 2009; Habier et al. 2010; Jannink et al. 2010 ; Grattapaglia and Resende 2011 ; Heffner et al. 2010 ) R ec ently, a number of analytical approaches ( Gianola et al. 2006; de los Campos et al. 2009 a ; Habier et al. 2011; Legarra et al. 2011 b ) have been developed to study factors that contribute to GS accuracy ( Habier et al. 2009; Habier et al. 2010 ; Iwata and Jann ink
21 2011 ) and to increase GS accuracy relative to the original approaches proposed by Meuwissen et al. ( 2001 ) Higher accuracy and less bias in the estimat ed BLUP BVs are expected to improve the accuracy of all GS models. However, the effect of correcting pedigree errors on BLUP BVs used to develop GS BV prediction models h a s not been assessed Here we report f or a loblolly pine breeding population, the effect of pedigree correction based on construction of a realized relationship matrix from a dense panel of genetic markers. The original and corrected pedigrees were used to generate BLUP BVs and posteriorly GS models using ridge regression BLUP. The accuracies of the uncorrected and corrected pedigrees on BLUP BV and GS BV were compared. Methods Data Pheno typic and genotypic data were collected from one field test located in Nassau (Florida, USA) containing 956 clonally propagated loblolly pine trees (~8 ramets per genotype) of a genetic test design with 61 families derived from 32 parents crossed in a circ ular mating design (details in Baltunis et al. 2005 ). The field site was established using single tree plots in eight replicates (one ramet in each replicate) utilizing a resolvable alpha incomplete block design ( Williams et al. 2002 ) Two silvicultural t reatments were applied; four replicates were grown under high intensity and four replicates under operational culture. Phenotype m easurements were taken for basal height of the live crown (BLC, cm), crown width across the planting beds (CWAC, cm), crown wi dth along the planting beds (CWAL, cm), stem diameter (DBH, cm) and total stem height (HT, cm) as described in Baltunis et al. (2007 a ) and Resende et al. (2012) The traits branch angle average (BA,
22 degrees) and average branch diameter (BD, cm) were measur ed only in the high in tensity silvicultural treatment. The age for each m e asurement is listed in Tabl e 2 1, together with the trait age combination used hereafter. G enomic DNA was extracted from n eedle tissue using the Q IAGEN DNeasy Plant Kit, and quantifi ed with a NanoDrop microvolume spectrophotometer One microgram of DNA from each clone was genotyped using an Diego, CA) designed detect 7,216 SNPs that were identified through the resequencing of 7 535 uniquely expr essed sequence tag (EST) contigs in 18 loblolly pine haploid megagametophytes ( Eckert et al. 2010 ) After filtering for monomorphic markers a total of 4,825 SNPs were selected for analysis. Realized Relationship Matrix and Pedigree C orrections A total of 2 ,182 SNP markers, with a minor allele frequency greater than 0.12, were used to construct the RRM. The RRM was estimated by determining identity by state coefficients relative to the parents of the current popula tion as the base population ( Powell et al. 2 010 ) Relatedness estimates were adjusted for sampling error and shrunk toward the expected values to lessen error as recommended by Yang et al. (2010) Using relationships estimated in the RRM, the pedigree was corrected based on the normality of the dist ribution of the relationship coefficients around their expected values (i.e. 0.5 for full sib). First, the RRM matrix was paired with the A matrix. Second, duplicated individuals (different label, but same genotype) were identified, and the ones with the f ewer missing values were kept. Third, the relationship coefficient limits for the full sib and half sib classes were defined based on the normal distribution using all relationships in each class. Fourth, individual or groups of individuals not matching th e expected pattern were identified. Fifth, conflictive individuals were re assigned to a new
23 pedigree by searching across all relationships in the dataset for the parent or family where these individuals match the expectation. In the last step, an individu al was re assigned to a new parent/family only if the conflictive individual matched the expectation, given by the defined boundaries, with all individuals from that parent/family. Once the new parent/family was identified, the individuals were re labeled generating the corrected pedigree. This process was iterative, as every time the pedigree of an individual was corrected the relationship class distributions changed across the database and were recalculated. BLUP/REML Analysis: V ariance Component Estimat ion a nd Breeding Values Prediction To investigate the effects of BLUP BV predictions on GS, two alternative linear mixed models were fitted independently using ASReml v.3.0 ( Gilmour et al. 2009 ) for each trait. Accuracy for all BLUP analyses was estimated based on the prediction error variance for each clone separately ( Mrode 2005 ) and the average was reported. Original pedigree BLUP (Ori BLUP) This model assumes no errors in the original pedigree (1) where y is the measure of the trait being analyze d (see above), b is a vector of fixed effects (i.e. culture type and replication within culture type), i is a vector of random incomplete block effect within replication ~N(0, I 2 iblk ), a is a vector of random additive effects of clones ~N(0, A 2 a ), f is a vector of random family effect ~N(0, I 2 f ), n is a vector of random non additive effects of clones ~N(0, I 2 n ), d 1 is a vector of random additive by culture type interaction ~N(0, DIAG 2 d1 ), d 2 is a vector of random family by
24 culture type interaction ~N(0 DIAG 2 d2 ), d 3 is a vector of random non additive by culture type interaction ~N(0, DIAG 2 d3 ), e is the random residual effect ~N(0, DIAG 2 e ) as one specific error for each treatment was fitted, X and Z 1 Z 7 are incidence matrices and I, A and DIAG are the identity, numerator relationship and block diagonal matrices respectively. Corrected pedigree BLUP (Corr BLUP) T his model assumes that the original pedigree contains errors that were corrected using the relationships derived from the R RM and implemented f or analysis in the corrected version of the pedigree. Therefore, in this analysis a corrected version of the A matrix will be used (A cor ). This analysis uses the same model described above (equation 1), although in this case a is a vector of random additi ve effects of clones ~N(0, A cor 2 a ). Genomic Selection and Validation The breeding value estimated in each of the above models was deregressed and the parental average of each family removed ( Garrick et al. 2009 ) for genomic selection analysis. The deregre ssed phenotype derived by using the original and the corrected pedigree was used as input for a ridge regression BLUP with the 4,825 markers used as covariates as described previously ( Resende et al. 2012b ) Each analysis was repeated 10 times in a cross v alidation scheme ( Kohavi 1995 ) The predictive ability of each model was estimated as the correlation between the genomic selection predicted breeding values (GS BVs) and the deregressed phenotype that were used as input in the generation of the GS BVs.
25 Re sults Pedigree C orrection The relationship coefficients derived from the molecular markers is expected to be a n ormal distribution centered at 0.5 and 0.25 for full and half sib families, respectively. The distribution with the original pedigree was bi mo dal and asymmetrical for half sibs, with a large frequency closer to the expected 0.25 value and a second peak close to zero (Figure 2 1 top left panel ) For the full sib class a tri modal asymmetrical distribution was observed the highest peak (mode) aro und the corrected 0.5 expectation value, with the second and third peaks around the 0.25 and a zero relationship, respectively (Figure 2 1 bottom left panel ) In the original pedigree, before corrections, the most frequent relationship fou nd in the dataset yielded biased average relationship coefficients (Table 2 2), with unrelated, half sibs, and full sibs ind ividuals being underestimated, and the diagonal being slightly overestimated. The standard deviations for full sib and half sib individuals were the largest (Table 2 2). However, correcting the pedigree gave mean values that agreed with the expectations for the given classes, causing a 27 to 67% decrease in the standard deviation (Table 2 2, Figure 2 1 right panels ). By using the RRM, different types o f pedigree errors were detected and corrected, including duplicated genotypes (clones) with different label s, from which only one was kept. Individuals with either one or both incorrect parents (sixty nine in total), were reassigned to the correct parent u sing the coefficients fro m the RRM. Eleven new parents, one female and ten male, were added, as they did not exist in the pedigree records. Parents of four complete families and two grandparents were reassigned.
26 Finally, three individuals were removed beca use they yielded inconsistent relationships across the pedigree (Table 2 3) E stimation of B reeding Value s with Original a nd Corrected Pedigree Relationship Matrices B oth the original and corrected pedigree s were used to estimate BV s from a traditional B LUP analysis. H eritability estimates derived from the REML/ BLUP analysis using the corrected pedigree decreased slightly for eight of the traits ( maximum decrease of 5% ), when compared with the REML/ BLUP analysis using the original pedigree. In seven trai t s the heritability increased by a maximum of 21% for BD_6 ( Table 2 4 ). Overall, with the corrected version of the pedigree, breeding value accuracy decreased slightly in only four traits with a maximum reduction of 0.94% for BA_6 The BV accuracy increase d for 11 traits ( maximum increase of 5.8% for HT_6 ). Importantly, in all but one trait (BLC_6) t he models with the corrected pedigree fit t he data substantially better, measured by the A kaike I nformation C riteria (AIC, Table 2 4). A ccuracy o f Genom ic Selec tion Predictive Models w ith Original and Corrected Pedigrees Breeding values obtained from BLUP an alyses with the original and corrected pedigrees were posteriorly deregres sed and used as response variables to generate genomic selection model s for the 15 t rait age combinations. T he predictive ability of the model s increase d for 13 of the 15 traits when the corrected version of the pedigree was used (Figure 2 2) The two traits that decreased with the corrected pedigree (BA_6 and CWAC_6) were reduced by 1.1 and 2.3%, respectively; whereas the predi c tive ability of the remaining 13 traits increased from 1 to 15% with an average of 7.2%
27 Discussion Pedigree C orrection Genetic improvement of trees is logistically complex, time consuming and expensive. Over the l ast 40 years, forest tree breeders have decreased breeding cycle time and improved the estimates of heritability of most traits which led to greater gains per cycle ( White et al. 2007 ) Most breeders calculate BLUP BVs from phenotypic information obtained from field trials with progeny from pedigreed breeding populations, to rank parents and progeny for selection. Despite these advances, it is still vital to decrease breeding cycle time and increase gain per cycle. The gain per cycle is affected by the accu racy of BLUP BV. Errors in the pedigree can lead to biased BLUP BV predictions, and have been estimated to average 10% ( Banos et al. 2001; Visscher et al. 2002; Doerksen and Herbinger 2010 ) although these vary from program to program. Correcting pedigree errors should improve BLUP BV predictions and improve heritability estimates. Pedigree errors have been corrected by genotyping (e.g. SSR fingerprinting) parents and progeny or from the diagonal of the realized relationship matrix to detect foreign popula tions ( Simeone et al. 2011 ) Here we propose the use of the normality property of the different relationship classes to correct errors in the pedigree. Recent advances in genotyping methods enable the rapid development of dense panels of molecular markers that, as we show, can be used to correct historical errors carried in the pedigree. The use of a dense panel of markers has the advantage of being a byproduct of the genomic selection objective. To correct errors, a realized relationship matrix ( Powell et al. 2010 ) is constructed for the breeding population. In the relationship matrix, a normal symmetric and uni modal distribution for each relationship class (i.e. unrelated, half sib or full sib) is
28 expected because of Mendelian sampling ( Simeone et al. 20 11 ) This has been observed with 294,831 SNPs markers on 3,925 human individuals with a standard deviat ion between 0.004 and 0.005 ( Yang et al 2010 ) As more markers are added more precise estimations of the Mendelian sampling will be obtained and, thus, smaller stand ard deviations are observed ( Hayes et al. 2009 a ) In our case, we detected a bi modal asymmetrical distribution for half sibs, indicating problems in the recorded pedigree and showing a bias for the mean relationship (see Figure 2 1). The addi tional peak observed in the distribution was centered on zero, indicating that unrelated individuals were being misclassified as half sibs. After re assignment of individuals and correction of pedigree, the expected normal distribution was observed, as wel l as a considerable decrease in the standard deviation. This also was the case for the full sib relationship class. Although we obtained a large decrease in the standard error, our estimations are still high compared with th ose obtained by Yang et al. (201 0) or Simeone et al. (2011) probably due to the reduced number of SNPs markers (~2,300) genotyped on a smaller population (~860 individuals) with many different relationship classes derived from the circular mating design (i.e. unrelated, half sibs, full sibs, etc.). Better estimations are expected as more markers and individuals are added in future studies. The extended length of a pine breeding cycle and their reproductive biology, contribute to a high likelihood of pedigree errors. Pines are wind pollin ated and pollen from foreign genotypes is commonly present during controlled pollinations. Similarly, the length of the breeding cycle implies that record keeping is prone to include errors (White et al. 2007) Most errors can be corrected by re assigning individuals, parents or
29 families present in the known pedigree, although the necessity of adding new parents ind icates pollen contamination (Adams et al. 1988 ) In our case, three individuals were dropped from further analysis as they yielded inconsistent relationships. These inconsistent relationships of these three individuals were due to large amounts of missing SNP data, indicating genotyping problems. Estimation of Breeding Value with Original and Corrected Relationship Matrices Independently of the s tage when the errors originated, our results show that pedigree errors decrease the accuracy of the BLUP BV prediction, as previously reported in pines and dairy cattle ( Ericss on 1999; Banos et al. 2001; Sanders et al. 2006 ) In addition to improved BLUP B V accuracy, using the corrected pedigree, instead of the original, dramatically increased the fit of the data (Table 2 4). This indicated that with the original pedigree the heritability was slightly overestimated in eight traits and underestimated in seve n (Table 2 4). The impact of correcting the pedigree on the BLUP analysis not only depends on the number of errors but also on how much difference existed between the phenotypic value of the individual, and the average of the family where the individual wa s incorrectly assigned. This happens because the traditional BLUP analysis shrinks the individual records towards the parental average of the family defined in the A matrix. When the phenotype of the mislabeled individual is similar to the family average i n which this individual was misassigned, the estimated breeding value will be less biased than in a situation where the difference between the phenotypic value and the average of the family is large. However, even in those cases, there are some practical c onsiderations regarding inbreeding and selection. If the best performing individuals are mislabeled, then related individuals may be selected inadvertently, or conversely, selection of superior unrelated
30 individuals may be avoided because they are labeled as the same family. Both cases will impact the potential genetic gain, the first through inbreeding depression and the second in the loss of opportunity of selection one of the best individuals. Accuracy of Genomic Selection Predictive Models with Original and Corrected Pedigrees Genomic selection offers the possibility to dramatically accelerate tree genetic improvement by eliminating, in some phases, the need of field tests to select superior individuals. Furthermore, selection of elite individuals can be more accurate compared to traditional phenotypic selection (Resende et al. 2012a) Many different methodologies have been proposed to construct GS prediction models with the aim of increasing their accuracy. However, for most quantitative traits there is not a clear advantage of any of the prop osed prediction methods ( Heslot et al. 2012 ; Resende et al. 2012b ) Nonetheless, other opportunities exist for improvement of the accuracy of GS prediction models. One approach adopted in this study was the improveme nt of the BLUP BV used as input for constructing the GS models by correcting errors in the pedigree. When BVs derived from the corrected pedigree were deregressed and used to construct GS models, the accuracy of these models increased for 13 of 15 traits. This included seven out of the eight traits that previously had a decrease in heritability in the BLUP analysis. This indicates that GS models more efficiently capture associations between markers and QTLs, when the correct pedigree is used to estimate BLU P BV. The traits BA_6 and CWAC_6 showed a smaller GS prediction ability with the new pedigree; however, these traits showed a slightly smaller or equal accuracy for the BLUP BV prediction and a high increase in data fitting (AIC) indicating that the origin al pedigree was overestimating the GS predictive ability in these two cases.
31 Table 2 1. Age of trait measurement and code trait age combination Trait Age measured Code Trait Age measured Code BA 6 BA_6 DBH 3 DBH_3 BD 6 BD_6 DBH 4 DBH_4 BLC 4 BLC_4 DBH 6 DBH_6 BLC 6 BLC_6 HT 1 HT_1 CWAC 2 CWAC_2 HT 2 HT_2 CWAC 6 CWAC_6 HT 3 HT_3 CWAL 2 CWAL_2 HT 6 HT_6 CWAL 6 CWAL_6 Table 2 2. Original and corrected pedigree mean and standard deviation for relationship classes in the population. Original Pedi gree Corrected Pedigree Relationship Class Expected Relationship Coefficient Mean Standard Deviation Mean Standard Deviation Unrelated 0.0000 0.0382 0.044 0 .0005 0.015 Half Sibs 0.2500 0.1974 0.089 0.2500 0.042 Full Sibs 0.5000 0.4563 0.121 0.5001 0 .061 Self 1.0000 1.0121 0.055 0.9997 0.040 Table 2 3. Number of individuals in each pedigree category in the original and new pedigree Category Original pedigree Corrected Pedigree Clones 956 940 Females 26 26 Males 27 37 Families 61 71
32 Table 2 4 Narrow sense heritability (h 2 m ), accuracy of breeding values (Acc(BV)) and fitting of models (log L = maximum of Log(likelihood), AIC= Akaike Information Criteria) by traditional BLUP analysis using a full genetic model with original pedigree or using a full genetic model with corrected pedigree (from eq. 1) on 15 trait age combination. Full Original Pedigree BLUP Full Corrected Pedigree BLUP Trait h 2 Acc(BV) Log L AIC h 2 Acc(BV) Log L AIC BA_6 0.33(0.08) 0.82 9056.1 18122.3 0.33(0.08) 0.81 9015.3 1 8040.7 BD_6 0.12(0.04) 0.69 2004.1 3998.2 0.15(0.05) 0.72 2003.5 3996.9 BLC_4 0.19(0.06) 0.78 8167.9 16353.8 0.22(0.02) 0.81 8044.6 16107.1 BLC_6 0.31(0.08) 0.79 37.7 65.4 0.35(0.03) 0.82 38.5 67.0 CWAC_2 0.23(0.02) 0.82 5355.0 10728.0 0.22(0.02 ) 0.82 5251.8 10521.6 CWAC_6 0.43(0.10) 0.85 4898.4 9806.8 0.45(0.02) 0.85 4834.6 9679.1 CWAL_2 0.21(0.02) 0.82 4779.5 9577.0 0.21(0.02) 0.82 4673.5 9365.0 CWAL_6 0.27(0.08) 0.79 3898.8 7807.6 0.27(0.03) 0.79 3838.3 7686.7 DBH_3 0.27(0.02) 0.83 4304.4 8626.9 0.26(0.02) 0.83 4292.3 8602.6 DBH_4 0.28(0.02) 0.83 6165.2 12348.5 0.27(0.02) 0.83 6146.8 12311.6 DBH_6 0.32(0.02) 0.85 7996.2 16010.3 0.31(0.02) 0.85 7971.0 15959.9 HT_1 0.11(0.03) 0.75 3727.4 7472.8 0.12(0.03) 0.77 3622.3 7262.6 HT_2 0.27(0.02) 0.82 29071.5 58160.9 0.27(0.02) 0.84 28950.9 57919.7 HT_3 0.28(0.08) 0.83 2593.0 5203.9 0.27(0.02) 0.84 2456.6 4931.2 HT_6 0.26(0.07) 0.80 5091.4 10194.8 0.31(0.02) 0.85 4944.6 9901.1
33 Figure 2 1. Distribution of relationship va lues for half sib and full sib individuals around their expected means 0.25 and 0.5, respectively. D istribution for the original pedigree ( a and c ) and corrected pedigree ( b and d ).
34 Figure 2 2. Predictive ability for fifteen different traits using the original pedigree derived from historical records (White column) and the corrected version of the pedigree (Grey column).
35 CHAPTER 3 ACCURACY OF GENOMIC SELECTION METHODS IN A STANDARD DATA SET OF LOBLOLLY PINE ( PINUS TAEDA L.) 1 Background Plant and anima l breeders have effectively used phenotypic selection to increase the mean performance in selected populations. For many traits, phenotypic selection is costly and time consuming, especially so for traits expressed late in the life cycle of long lived spec ies. Genome Wide Selection (GWS) ( Meuwissen et al. 2001 ) was proposed as an approach to accelerate the breeding cycle. In GWS, trait specific models predict phenotypes using dense molecular markers from a base population. These predictions are applied to genotypic information in subsequent generations to estimate Direct Genetic Values (DGV). Several analytical approaches have been proposed for genome based prediction of genetic values, and these differ with res pect to assumptions about the marker effects ( de los Campos et al. 2009a ; Habier et al. 2011 ; Meuwissen et al. 2001 ) For example, Ridge Regression Best Linear Unbiased Prediction (RR BLUP) assumes that all marker effects are normally distributed, and that these marker effects have identical variance ( Meuwissen et al. 2001 ) In Bayes A, markers are assumed to have different variances, and are modeled as following a scaled inverse chi square distribution ( Meuwis sen et al. 2001 ) The prior in Bayes B ( Meuwissen et al. 2001 ) assumes the probability (1 square dist ribution, with v degree of freedom and scale parameter S 1 Chapter published in Genetics, Vol. 190, 1503 1510 April 2012
36 architecture of the trait suggesting an improvement to the Bayes B model, known as prior uniform distribution ( Habier et al. 2011 ) A drawback of Bayesian methods is the n eed for the definition of priors. The requirement of a prior for LASSO method, which needs less information ( de los Campos et al. 2009b ; Legarra et al. 2011b ) Methods for genomic prediction of genetic values may perform differently for different phenotypes ( Habier et al. 2011 ; Meuwissen et al. 2001 ; Usai et al. 2009 ) and results may diverge because of differenc es in genetic architecture among traits ( Grattapaglia and Resende 2011 ; Hayes et al. 2009 b ) Therefore it is valuable to compare performance among methods with real data and identify those which provide more accurate predictions. Recently, GWS was applied to agricultural crops ( Crossa et al. 2010 ) and trees ( Resende et al. 2011 ) Here we report, for an experimental breeding population of the tree species loblolly pine ( Pinus taeda L.), a comparison of GWS predictive models for 17 tra its with different heritabilities and predicted genetic architectures. Genome wide selection models included RR addition, we evaluated a modified RR BLUP method that utilizes a subset of selected markers, RR BLUP B. We show that, for most traits, there is limited difference among for fusiform rust resistance a disease resistance trait showed previously to be controlled in part by major genes and the proposed method RR BLUP B was similar to to the model
37 Materials and M ethods Training Population a nd Genotypic Data The loblolly pine population used in this anal ysis is derived from 32 parents representing a wide range of accessions from the Atlantic Coastal Plain, Florida and Lower Gulf of the United States. Parents were crossed in a circular mating design with additional off diagonal crosses, resulting in 70 ful l sib families with an average of 13.5 individuals per family ( Baltunis et al. 2007a ) This population is referred to hereafter as CC LONES (Comparing Clonal Lin es On Experimental Sites). A subset of the CCLONES population, composed of 951 individuals from 61 families (mean = 15, San Diego, CA ; Eckert et al. 2010 ) with 7,216 SNP, each representing a unique pine EST contig. A subset of 4,853 SNPs were polymorphic in this population, and were used in this study. None of the markers were excl uded bas ed on minimum allele frequency. P henotypic D ata The CCLONES population was phenotyped for growth, developmental and disease resistance traits in three replicated studies. The first was a field study established using single tree plots in eight repl icates (one ramet of each individual is represented in each replicate) that utilized a resolvable alpha incomplete block design ( Williams et al. 2002 ) In that field trial, four replicates were grown under a high intensity and four were grown under a standard silvicultural intensity regime. The traits stem diameter (DBH, cm), total stem height (HT, cm) and total height to the base of the live crown (HTLC, cm) were measured in the eight replicates at ye ars 6, 6 and 4, respectively. At year 6, crown width across the planting beds (CWAC, cm), crown width
38 along the planting beds (CWAL, cm), basal height of the live crown (BLC, cm), branch angle average (BA, degrees) and average branch diameter (BD, cm) were measured only in the high intensity silvicultural treatment. Phenotypic traits tree stiffness (Stiffness, km 2 /s 2 ), lignin content (Lignin), latewood percentage at year 4 (LateWood), wood specific gravity (Density), and 5 and 6 carbon sugar content (C5C6 ) were measured only in two repetitions, in the high intensity culture ( Baltunis et al. 2007a ; Emhart et al. 2 007 ; Li et al. 2007 ; Sykes et al. 2009 ) The second study was a greenhouse disease resistance screen. The experimental design was a randomized complete block with single tree plots arranged in an alpha lattice with an incomplete block (tray container). Fusiform rust ( Cronartium quercuum Berk. Miyable ex Shirai f. sp. fusiforme ) susceptibility was assessed as gall volume (Rust_gall_vol) and presence or abs ence of rust (Rust_bin) ( Kayihan et al. 2005 ; Kayihan et al. 2010 ) Finally, in the third study the rooti ng ability of cuttings was investigated in an incomplete block design (tray container) with four complete repetitions, in a controlled greenhouse environment. Root number (Rootnum) and presence or absence of roots (Rootnum_bin) were quantified ( Baltunis et al. 2005 ; Baltunis et al. 2007b ) Breeding Value Prediction Analyses were carried out using ASReml v.2 ( Gilmour et al. 2006 ) with the following mixed linear model: Where y is the phenotypic measure of the trait being analyzed, b is a vector of the fixed effects, i is a vector of the random incomplete block effects within replication ~N(0,
39 I 2 iblk ), a is a vector of random additive effects of clones, ~N(0, A 2 a ), c is a vector of random non additive effects of clones ~ N (0, I 2 c ), f is a vector of random family effects ~N(0, I 2 f ), d 1 and d 2 are described below, e is the vector of random res idual effects ~N(0, DIAG 2 e ), X and Z 1 Z 6 are incidence matrices and I, A and DIAG are the identity, numerator relationship and block diagonal matrices, respectively For traits measured in the field study under both high and standard culture intensities, the model also included d 1 a vector of the random additive x culture type interaction ~N(0, DIAG 2 d1 ), and d 2 a vector of the random family x culture type interaction ~N(0, DIAG 2 d2 ) Narrow sense heritability was calculated as the ratio of the additive variance 2 a to the total or phenotypic variance (e.g. for the field experiment total variance was 2 a + 2 n + 2 f + 2 d1 + 2 d2 + 2 e ). Prior to use in GWS modeling, the estimated breeding values were deregressed into phenotypes (DP) following the approach describe d in Garrick et al. (2009 ) to remove parental averag e effects from each individual. Statistical Methods The SNP eff ects were estimated based on five different statistical methods: RR BLUP, Bayes A ( Meuwissen et al. 2001 ) ( Habier et al. 2011 ) the Improved Bayesian LASSO (BLASSO) approach proposed by Legarra et al. (2011b ) and RR BLUP B (a modified RR BLUP). In all cases the genotypic information was fitted using the model: Where DP is the vector of phenotypes deregressed from the additive genetic values ( Garrick et al. 20 09 ) is the overall mean fitted as a fixed effect, m is the vector of
40 and Z is the incidence matrix m constructed from covariates based on the genotypes. No additional information, such as marker location, polygenic ef fects, or pedigree was used in those models. Once the marker effects were estimated using one of the methods, the predicted direct genetic value (DGV) of individual j for that method was given by: Where i is the spec ific allele of the i th marker on individual j and n is the total number of markers. Random Regression Best Linear Unbiased Predictor (RR BLUP) The RR BLUP assumed the SNP effects, m, were random ( Meuwissen et al 2001 ) The variance parameters were assumed to be unknown and were estimated by restricted maximum likelihood (REML), which is equivalent to Bayesian inference using an uninformative, flat prior. The first and second moments for this model are describe d below: w here is the variance common to each marker effect and is the residual variance. The mixed model equation for the prediction of m is equivalent to: Where refers to the total additive variance of the trait and due to standardization of the Z matrix, refers to the total number of markers ( Meuwissen et al. 2009 ) The matrix Z was parameterized and standardized to have a mean of zero and variance of
41 one as previously described ( Resende e t al. 2010 ; Resende et al. 201 2 a ) The analyses were performed in the software R (available at CRAN, http://cran.r project.org/) Bayes A The Bayes A method proposed by Meuwissen et al. (2001 ) assumes the conditional distribution of each effect (given its variance) to follow a normal distribution. The variances are assumed to follow a scaled inversed chi square distribution with degrees of freedom and scale parameter S 2 a The unconditional distribution of the marker effects can be shown to follow a t distribution with mean zero ( Sorensen and Gianola 2002 ) Bayes A differs from RR BLUP in that each SNP has its own variance. In this study, was assigned the val ue 4, and S 2 a was calculated from the additive variance according to Habier et al. (2011 ) as follows: where: and p k is the allele frequency of the k th SNP. Habier et al. (2011 ) In this method, the SNP effects have a common variance, which follows a scaled inverse chi square prior with parameters S 2 a. As a result, the effect of a SNP fitted with probability (1 distributions, t(0, I S 2 a of a marker having zero effect. Parameters and S 2 a were chosen as described fo r Bayes A and Bayes C were performed using the software GenSel ( Fernando and Garrick 2008 ) ; available at http://bigs.ansci.iastate.edu/bigsgui/) for which an R
42 package is available in the Supporting Inf ormation (File S5). The marker input file was coded as 10, 0 and 10 for marker genotypes 0,1 and 2, respectively. A total of 50,000 iterations were used, with the first 2,000 excluded as the burn in. Bayesian LASSO The Bayesian LASSO method was performed as proposed by Legarra et al. (2011b ) using the same model equation used previously for the estimation of the markers effects. However, in this case: ; Using a formulation in terms of an augmented hierarchical model including an extra variance component associated to each marker locus, we have: t herefore, The prior distribution for 2 e was an inverted chi square distribution with 4 degre es of freedom and expectations equal to the value used in regular genetic evaluation for 2 e Analyses were performed using the software GS3 ( Legarra et al. 2011a ) ; available in http://snp.toulouse.inra.fr/~alegarra/. The chain length was 100,000 iterations, with the first 2,000 excluded as the burn in and a thinning interval of 100. RR BLUP B We also evaluated a modified, two step RR BLUP method that reduces the number of marker effects estimated. In this case, the DGV for each trait was generated
43 based on a reduced subset of markers. In order to define the number of markers in the subset, the marker effects from the RR BLUP were ranked in decreasing order by their used, with their origina l effects, to estimate DGV. The size, q of the subset that maximized the predictive ability was selected as the optimum number of marker effects to be used in subsequent analyses. Next, markers effects were re estimated in a second RR BLUP, using only the selected q markers within each training partition (see below). The estimated effects derived from this analysis were used to predict the merit of the individuals in the validation partition that were not present in the training partition. This process was repeated for different allocations of the data into training and validation partitions. In each validation, a different subset of markers was selected, based on the highest absolute effects within that training partition. Therefore, the only restriction a pplied to the second analysis was related to q the number of markers to be included in each dataset. The same approach was performed with two additional subsets of markers of the same size as a control: the first subset contained randomly selected markers and the second subset contained markers with the smallest absolute effect values. Validation of the models Two cross validation schemes were tested in the RR BLUP method: 10 fold and leave one out. For the 10 fold cross validation approach a random sub sa mpling partitioning, fixed for all methods, was used ( Kohavi 1995 ) Briefly, the data for each trait were partitioned into two subsets. The first one was composed by the majority of the individuals (90%) and was used to estimate the marker effects. The second one, the validation partition (10%), had their phenotypes predi cted based on the marker effects
44 estimated in the training set. Randomly taken samples of N= (9/10) x N T individuals were used as training sets, while the remaining individuals were used for validation (N T = total number of individuals in the population). T he process was repeated ten times, each time with a different set of individuals as the validation partition, until all individuals had their phenotypes predicted ( Legarra et al. 2008 ; Usai et al. 2009 ; Verbyla et al. 2010 ) In the leave one out approach, a model was constructed using N T 1 individuals in the train ing population and validated in a single individual that was not used in the training set. This was repeated N T times, such that each individual in the sample was used once as the validation individual. This method maximized the training population size. A ccuracy of the models The correlation between the Direct Genetic Values (DGV) and the Deregressed Phenotype (DP) was estimated using the software ASReml v.2 ( Gilmour et al. 2006 ) from a bivariate analysis, including the validation groups as fixed effects since each validation group had DGV estimated from a different prediction equation and might have had a differe nt mean. This correlation represented the predictive ability ( ) of GS to predict phenotypes, and was theoretically represented ( Resende et al. 2010 ) by: where was the accuracy of GS and h was the square root of the heritability of adjusted phenotypes, which is associated to Mendelian sampling effects and is given by where n was the number of ramets used in each study. To remove the influence of the heritability upon the predictive ability and thus estimate the accuracy, the following formula was applied
45 In addition, for each metho d and trait, the slope coefficient for the regression of DP on DGV was calculated as a measurement of the bias of the DGV. Unbiased models are expected to have a slope coefficient of 1, whereas values greater than 1 indicate a biased underestimation in the DGV prediction and values smaller than indicate a biased overestimation of the DGV. Results Cross Validation Method Testing the effect of cross validation using two methods, 10 fold and leave one out (N fold), showed that their predictive ability was not significantly different ( Table A 1 ) The largest difference was detected for the trait CWAC, where the leave one out method outperformed the 10 fold cross validation by 0.02 (standard error = 0.03). Likewise, no significant differences were found for bias of the regressions (slope) in both methods (Table A 2). Thus, the 10 fold approach was selected and used for comparing all methods. Predictive Ability of t he Methods Four well established genome wide selection methods were compared in 17 traits with herita bilities ranging from 0.07 to 0.45. Overall, the ability to predict phenotype ( ranged from 0.17 for Lignin to 0.51 for BA (Table 3 1). Although the methods differ in a priori assumptions about marker effects, their predictive ability was simil ar no significant differences were detected for any of the 17 traits. The standard errors for each method and trait are described in (Table A 3).
46 Bayesian approaches performed better for traits in the disease resistance category. For Rust_bin, the method RR superior to RR BLUP and BLASSO. The accuracy for each genome wide prediction method was also estimated, and varied from 0 .37 0.77 (Table A 4). For all methods, the ability to predict phenotypes ( was linearly correlated with trait heritability. The strongest correlation (0.79) was observed for RR BLUP (Figure 3 1). The correlation is expected, as traits with lowe r heritability have phenotypes less reflective of their genetic content, and are expected to be less predictable through genomic selection. Bias of the M ethods The coefficient of regression (slope) of DP on DGV was calculated as a measurement of the bias o f each method. Ideally, a value of beta equal to one indicates no bias in the prediction. For all traits, the slopes of all the models were not significantly different than one, indicating no significant bias in the prediction. In addition, no significant differences among the methods were detected (Table A 5) Although no evidence of significant bias was detected, the value of beta derived from RR BLUP was slightly higher for all traits (average across traits equal to 1.18). Markers Subset and RR BLUP B Pr ediction of phenotype was also performed with RR BLUP, but adding increasingly large marker subsets, until all markers were used jointly in the prediction. The predictive ability was plotted against the size of the subset of markers (Figure 3 2). The patte rn of the prediction accuracy was similar for 13 out 17 traits (Figure 3 2 left ),
47 where differences were mainly found in the rate with which the correlation reached the asymptote. In these cases, the size of the subset ranged from 820 to 4,790 markers. How ever, a distinct pattern was detected for disease resistance related traits, density and CWAL (Figure 3 2 right ). In these cases, maximum predictive ability was reached with smaller marker subsets (110 590 markers), and decreased with the addition of more markers. An additional RR BLUP was performed using as covariates only the marker subset for which maximum predictive ability was obtained. For traits where a large number of markers (> 600) explain the phenotypic variability, RR BLUP B was similar to RR BL UP or Bayesian methods (Table A 6) However, for traits where the maximum predictive ability (Density, Rust_bin, Rust_gall_vol) was reached with a smaller number of marker (<600), RR BLUP B performed significantly better than RR BLUP. For example, the pred ictive ability of the trait Rust_gall_vol was 61% higher using RR BLUP B (0.37) compared to the traditional RR BLUP (0.23), and also We also contrasted these results with the predictiv e ability using a subset of markers of similar size, but selected either randomly or to include those markers with lower effects. As expected, for the three traits the predictive ability was larger for the subset selected by RR BLUP B over the subsets with lower effects and random effects (Figure 3 3). A significant difference over the lower and random subsets was found for rust resistance related traits (Rust_bin, Rust_gall_vol), while for Density the markers selected by RR BLUP B were only significantly d ifferent than the lower marker subset but not different to the random marker subset.
48 Discussion We characterized the performance of RR BLUP/RR BLUP B, Bayes A, Bayesian resistance and biomass quality traits in common dataset generated from an experimental population of the conifer loblolly pine. In general, the methods evaluated differed only modestly in their predictive ability (defined by the correlation between the DGV and DP). The s uitability of different methods of developing GWS predictive models is expected to be trait dependent, conditional on the genetic architecture of the characteristic. RR BLUP differs from the other approaches used in this study in that the unconditional var iance of marker effects is normally distributed, with the same variance for all markers ( Meuwissen et al. 2001 ) This assumption may be suitable when considering an infinitesimal model ( Fisher 1918 ) where the characters are determined by an infinite number of unlinked and non epistatic loci, with small effect. Not surprisingly, BLUP based methods underperformed relative to Bayesian appr oaches for oligogenic traits. For instance, Verbyla et al. (2009 ) showed that BLUP based GWS had lower accuracy, compared to Bayesian methods, in prediction of fat percentage in a population where a single gene explains ~50% of the genetic variation. Similarly, our resistance traits, compared to RR BLUP, may reflect a simpler genetic architecture, with a few loci of large effect. While the causative genes that regulate fusiform rust resistance have not yet been uncovered, several genetic studies support the role of few major genes in the trait variation. For example, the Fr1 locus confers resistance to
49 specific fungus aeciospore isolates ( Wilcox et al. 1996 ) and at least five families within the CCLONES population segregate for this locus ( Kayihan et al. 2010 ) The under performance of RR BLUP for predicting oligogenic traits is a consequence of fitting a large number of makers to model variation at a trait controlled by few maj or loci, leading to model over the shrinkage of effects is marker specific, while in BLUP all markers are penalized equally. To address this limitation, we proposed an alternative, RR BLUP B, to Bayesian and the t raditional RR BLUP approaches, aimed at reducing the number of parameters. In RR BLUP B, marker effects are initially estimated and ranked using RR BLUP. Next, increasing markers subsets that include initially those with larger effect are used to estimate DGV. The number of markers that maximizes the predictive ability is then defined, and used in a second RR BLUP model. For rust disease resistance and wood density traits, the modified RR BLUP B approach performed better that traditional RR BLUP, and as wel l as the Bayesian methods. Previous studies using simulated data have shown that improvements in predictive ability could be obtained by using a similar approach to the one proposed here (Zhang et al. 2010, Zhang et al. 2011), although with a different str ategy of marker selection. While RR BLUP B may add an additional step to the development of predictive models (i.e. initial marker selection), it is overall simpler and computationally less expensive than Bayesian approaches. Therefore, it may provide a su itable alternative to the use of BLUP based methods for traits that do not fit an infinitesimal model, and are rather regulated by few major loci.
50 Table 3 1. Predictive ability of Genomic Selection models using four different methods; h 2 is the narrow se nse heritability of the trait. Trait category Trait h 2 Methods RR BLUP BLASSO Bayes A Bayes C Growth HT 0.31 0.39 0.38 0.38 0.38 HTLC 0.22 0.45 0.44 0.44 0.44 BHLC 0.35 0.49 0.49 0.49 0.49 DBH 0.31 0.46 0.46 0.46 0.46 Development CWAL 0.27 0.38 0.36 0.36 0.36 CWAC 0.45 0.48 0.46 0.47 0.47 BD 0.15 0.27 0.25 0.27 0.27 BA 0.33 0.51 0.5 1 0.51 0.51 Rootnum_bin 0.10 0.28 0.28 0.27 0.28 Rootnum 0.07 0.24 0.26 0.25 0.24 Disease resistance Rust_bin 0.21 0.29 0.28 0.34 0.34 Rust_gall_vol 0.12 0.23 0.24 0.28 0.29 Wood quality Stiffness 0.37 0.43 0.39 0.42 0.42 Lignin 0.11 0.17 0.17 0 .17 0.17 LateWood 0.17 0.24 0.24 0.23 0.24 Density 0.09 0.20 0.22 0.23 0.22 C5C6 0.14 0.26 0.25 0.25 0.25
51 Figure 3 1 Regression of RR BLUP predictive ability on narrow sense heritability for 17 traits (trend line is shown, R 2 =0.79)
52 Figu re 3 2 Example of the two patterns of predictive ability observed among traits, as an increasing number of markers is added to the model. Each marker group is repre sented by a set of 10 markers. a ) For DBH, the maximum predictive ability was detected when 380 groups of markers (3,800 marker s) were included in the model. b ) For the trait Rust_gall_vol, predictive ability pattern reached a maximum when only 10 groups (100 markers) were added. Lines indicate the predictive ability of RR BLUP (filled line), Ba and RR BLUP B (dotted line) as reported on Table 1 and in Supporting Information Table S6. a b
53 Figure 3 3 Predictive ability for subsets of 310 markers for Rust_bin, 110 markers for Rust_gall_vol and 240 markers for Density. Subset s were generated selecting markers with the lowest absolute effects (light grey), with random values (grey), including all markers (dark grey), and including only those markers with largest absolute effects (black).
54 CHAPTER 4 THE RE DISCOVERY OF NON ADDI TIVE EFFECTS WITH GENOMIC RELATIONSHIP MATRICES AND ITS IMPLICATION IN BREEDING 1 Background Non additive effects have been often neglected in animal and plant breeding, mainly because their variance estimates are usually small and non significant compared to the additive effect (Hill et al. 2008). Consequently, many breeding programs rely only on additive values ( breeding values ) to make progress from selection, completely ignoring dominance and epistasis. P artition ing genetic variance into additive, domina nce and epistasis is not always possible because the estimations are highly correlated (Hill 2010) and confounded with each other (Lynch and Walsh 1998). D epending on the gene frequencies involved, non additive allelic effects could greatly inflate the add itive variance estimates (Lu et al. 1999; Zuk et al. 2012) and the refore impact breeding value (BV) predictions (Palucci et al. 2007; Vanderwerf and Deboer 1989). In addition, the proper partition ing of variance components generate s a basic understanding o f the genetic architecture of t rait s which in turn help s to define the breeding strategy that would maximize genetic gains. Thus, for traditional breeding programs, ignoring existing non additive effects can negatively impact progress in t hree ways: 1) in flating the heritability and breeding values leading to overestimate of genetic gain 2) the variability due to non additive effects cannot be exploited in the next generation as the program selects by breeding values, and 3 ) if family or clonal propagatio n is possible in the breeding program, then there will be loss es in the potential to exploit this variability and reach the maximum possible genetic gain 1 Manuscript prepared to be submitted to Genetics Journal
55 T o partition the genetic variation into additive and dominance in breeding populations mating design s with at least full sib relationships are needed. Furthermore, to partition at the epistatic level requires either inbr ed or vegetative ly propagated (clonal) populations. In perennial plants with long r otations (> 5 years), inbr eds are not used b ecause of the generation length and the often high amount of inbreeding depression leaving clonal populations as the only option to explore the full genetic architecture (Foster and Shaw 1988). Several studies with clonal populations hav e been performed (Foster an d Shaw 1988; Mullin et al. 1992; Wu1996; Isik et al. 2003, 2005; Costa e Silva et al. 2004, 2009; Baltunis et al. 2007 b 2008, 2009; Araujo et al. 2012) with the aim of partition ing genetic variance using traditional pedigree based quantitative genetics appr oaches All these studies obtained small estimated values for dominance variation and often null or negative values for epistasis variation Furthermore, work by Hill et al. (2008) demonstrated that either all genetic variance is due to additive effects o r if n on additive effects are present they will be at least partially captured as additive variation. Currently, the use of molecular markers has become a popular way to predict BVs with genomic selection (GS) models Many analytic methodologies have been proposed with the aim o f increasing the accuracy of prediction. However, no significant differences have been detected among methods for quantitative complex traits (Resende et al. 2012b; Heslot et al 2012). The use of molecular mark ers for estimation of the additive relationships among individuals in a population, called realized relationship matrix (A G or Observed/Genomic Relationship Matrix) and its use instead of the numerator relationship matrix (A) in BLUP analysis (GBLUP) is one of the
56 proposed me thod s to predict BVs (Habier et al. 2010; Hayes et al. 2009; Veerkamp et al. 2011). Given that no large differences exist among methods, GBLUP will likely become the most popular way for predicting genomic BV (Aguilar et al. 2010), as BLUP is a well know n easily understood methodology and is equivalent to ridge regression BLUP (RR BLUP) (VanRaden 2008). In addition, as GBLU P has equivalent properties to BLUP an extended animal model can be fitted to incorporate dominance and epistatic effects, replacing t he pedigree derived non additive relationship matrices (Mrode 2005) with the marker derived counterpart. Use of A G instead of the numerator relationship matrix (A) derived from the pedigree improves estimates because A G better describe s the true relationsh ips among individuals known to be related by providing an estimat e s of Mendelian sampling and relationship s of individuals not previously known to be related. In addition, t he A G matrix combined with the A matrix (Aguilar et al. 2010) yield s more accurate estimates of variance components (Chen et al. 2011; Veerkamp et al. 2011). Finally, it has been shown that use of the A G instead of A matrix better separates genetics from environment al effects (Lee et al. 2010) We hypothesize that use of marker derived r elationship matrice s will allow better separation of the genetic variance components, revealing the genetic architecture of complex quantitative traits. The objective of this study was to test the use of molecular marker derived additive and non additive r elationship matrices for partition ing genetic variance components. For tree height, a trait with complex inheritance, we compare d in a clonal population of Pinus taeda different BLUP models under additive and full (additive plus non additive) assumptions w ith the use of either the pedigree derived relationship matrix or the marker derived matrices.
57 Materials and M ethods Data Total tree height (HT, m) measured at yea r 6 from a single field trial of the CCLONE S population (see Baltunis et al. 20 05 for detail s) was used in t he present study. In summary, 32 parents were crossed in a circular mating design with additional off diagonal crosses, resulting in 70 full sib families with an average of 13.5 individuals per family (Munoz et al. 2012) The clonal field t rial was establ ished using single tree plots with eight replicates (one ramet per replicate) in a resolvable alpha incomplete block design (Williams et al. 2002). Four of the replicates were grown under high intensity silviculture while the rest were under standard silviculture regime. A subset of the CCLONES population, composed of 951 individuals from 61 families were genotyped using an Illumina (Eckert et al. 2010) with 7,216 SNP s each representing a unique pine EST contig. A subset of 4,853 SNPs were polymorphic in this population. Relationship M atrices Out of the polymorphic markers a total of 2,182 SNPs markers had a minor genotype frequency greater than 0.12. This subset was used to estimate A G following the method proposed by Powell et al. (2010) where identity by descent coefficients are determined relative to the parents of the current population as the base population. The relationship values from A G were adjusted as recommended by Yang et al. (2010) to le ssen est imation error. The resulting A G was used to correct the pedigree as detailed in Munoz et al. (2012). Also, a molecular marker derived dominance relationship matrix ( D G ) was con s tructed. To build a dominance relationship matrix, a dominance incidenc e matrix ( W ) was created where a new codification was established for the genotypic file
58 containing all the polymorphic SNPs. Thus W h as the dimension n individuals times m markers and was re parameterized to be coded 1 if the genotype was heterozygous an d 0 if the marker genotype was homozygous for either class ( MM and mm) The matrix W was further standardized to a mean of 0. This was done by calculating the expectation of W. j for the j th marker derived as 2p j q j Thus W ij for the i th individual and j t h marker received the code: W ij = 1 2p j q j if the individual is heterozygous W ij = 0 if the individual has a missing data W ij = 0 2p j q j otherwise. Starting from the matrix W, the dominance relationship matri x was constructed us ing the following expressi on : where the denominator is the variance of W ij In addition, relationship matrices were obtained from the pedigree for additive relationships (A) and dominance relationships (D) following traditiona l methods (Lynch and Walsh 1998; Mrode 2005). The Hadamard product (#) between matrices was used to obtain the epistasis relationship matrices additive by additive (A # A), dominance by dominance (D#D ) and additive by dominance (A #D ) interaction for pedigree derived and markers derived A G #A G D G #D G and A G #D G respectively. Genetic Analyses All analyses were carried out in the software ASReml v3.0 (Gilmour et al. 2009), a genetic statistics software for fitting mixed model s on complex datasets using the spars e matrix methods and equipped with the Residual Maximum Likelihood (REML) for
59 variance component estimation using the average information algorithm (Gilmour et al. 1995). Six models were fitted using the pedigree derived matrices (models 1 to 6) and anothe r equivalent six models using the marker derived matrices (models 7 to 12 ), from the simpler (additive) to the more complex (additive plus dominance plus two way epistasis interaction). T he model including all terms (model 6 or 11) is show below where y is the phenotypic HT measure, is a vector of the fixed effects (i.e. silvicultural treatment and replicate), i is a vecto r of the random incomplete block effects within replication ~N(0, I 2 i ), is a vector of random additive effects of individuals ~N(0, B 1 2 a ), t 1 is a vector of the random additive by silviculture type interaction ~N(0, B 1 I 2 t1 ), d is a vector of random dominance effect of individual ~N(0, B 2 2 d ), t 2 is a vector of the random dominance by silviculture type interaction ~N(0, B 2 I 2 t2 ), is a vector of the random a dd itive by additive interaction ~N(0, B 1 # B 1 2 iaa ), is a vector of the rando m dominance by dominance i nteraction ~N(0, B 2 # B 2 2 idd ), is a vector of the random additive by dominance interaction ~N(0, B 1 # B 2 2 iad ) and e is the vector of random residual effects ~N(0, I 2 e ).The incidence matrices are X Z 1 Z 8, while I is the i dentity matrix and represent the Kronecker product and # the Hadamard product The matrix B 1 and B 2 c orresponded to an additive and dominance relationship matrices either derived from the pedigree replaced for A and D or from the markers replaced for A G and D G respective. Under this model the narrow sense heritability is the dominance to total variance ratio the epistatic to total variance ratio and
60 the broad sense heritability where is the estimated additive variance, is the estimated dominance variance and and are the total, epistatic and genet ic variance, res pectively. The definition of the last three variance estimates varied accordingly to the model being fit ted (see below for details). Model 1 ( A_ped ) and 7 ( A G _MM ) were fitted with only the additive effect and its interaction with silviculture. Thus, the es timated additive variance ( equals the genetic variance component ( as in this model non additive effects are ignored and the total variance is Model 2 ( D_ped ) and 8 ( D G _MM ) included addi tive and dominance effects. Thus, the estimated additive variance plus dominance variance estimation ( equals the genetic variance component as epistasis effect is ignored and the total variance is Model 3 ( A # A_ped ) and 9 ( A G #A G _MM ) expanded model 2 to include epistasis as additive by additive interaction. Here the genetic variance component i s the total variance is and the epistatic variance Model 4 ( D # D_ped ) and model 10 ( D G #D G _MM ) are similar to model 3 but replace the epi stasis effect by dominance by dominance int eraction while model 5 ( A# D_ped ) and model 11 ( A G # D G _MM ) are similar to model 3 but replace the epistasis effect by additive by dominance interaction Final ly, model 6 ( FULL_ped ) and model 12 ( Full_MM ) inclu des all effects mentioned above, i n this model where and the total variance is A summary of all models is presented in Table 4 1.
61 T esting and Validation of M odels The Akaike Information Criteria (AIC) was used to compare model fitting (Akaike 1974). The capacity of the different parameterizations to partition the variances estimated by the different models was evaluated using the sampling correlation matrix ( R ) among variance components estimates (Lee et al. 2010). The variance covariance matrix of estimated varianc e components ( V ) was used to estimate R as where L is the diagonal of the V matrix. The prediction ability of the different models was tested with a 10 fold cross validation with a random sub sampling partitioning fixed for all models (Kohavi 1995). Briefly, the genotyp e s were partitioned in 10 groups, thus each model were run 10 times with different 9 groups for constructing the model and the 10th group to validate the model At the end, all genotypes had their BV predicted from the model (PBV). On the other hand the BV derived from the models using the complete dataset in each model w ere assumed to be the real BV (RBV). The predictive ability of each model was tested as the correlation between RBV and PBV, and between predicted (PR) and real rankings (RR) for the top 10 % genotypes, emulating an operational selection scenario. Results T able 4 2 summarizes t he variance components, genetic parameters and indicators of data fitting, estimated with each of the twelve alternative models Compared to the A_ped model t he A G _MM model narrow and broad sense heritability (as non additive effects were ignored) increased slightly with both larger than 0.40. Including dominance effect s in the pedigree based model ( D_ped) decrease d h 2 by approximately 26% and the dominance ratio (d 2 ) was small ( 0.07 ) and non significant ly different from zero (2*SE(d 2 )>0.08). When the dominance effect was included with the
62 molecular marker based model ( D G _MM) h 2 decrease d 47% to 0.24 d 2 estimation increased to 0.16, a highly significant ly di fference from zero and a 70% of the additive value. With this model the dominance variance represent s 40% of the total genetic variation. We further extended these models to include the additive by additive, dominance by dominance and additive by dominance two way epistatic interaction factor s in three separate models. In pedigree based models with epistasis ( A # A_ped, D # D_ped and A # D_ped ) the estimations of variance components for additiv e and dominance varied slightly from those of the D_ped model. Moreover, in th ese three cases the estimation of epistasis was zero T he model including the additive by additive epistatic interaction (A G #A G _MM ) could not be fit and a reduced version dropping the culture by epistatic interaction factor was fitted instead. In the A G #A G _MM model t he additive and dominance ratios (h 2 and d 2 ) dropped considerably, while the epistatic interaction increased to 0.23 When the dominance by dominance and additive by dominance interaction s were added in model s D G #D G _MM and A G #D G _MM, respectivel y, the additive component dropped more than 30% and the dominance dropped 88% with respect to the D G _MM model, while the epistatic ratio (i 2 ) was estimated at 0.15 and 0.17 for the D G #D G _MM and A G #D G _MM respectively. Finally, a full model including addit ive, dominance and all two way epistatic interactions was fitted for pedigree (Full_ped) and marker based (Full_MM). In the case of the pedigree, the full model did not converge and a reduced version including additive, dominance, additive by additive and dominance by dominance was fitted. In this model the additive component decrease d slightly from 0.30 (in the D_ped model) to 0.27, the dominance was estimated to be zero and the epistasis (as the sum of both two way interactions )
63 was estimated close to 0.1 0. The estimation of variance components with the full marker based model (Full_MM) was similar to the A G #D G _MM model. Under this model the epistatic interaction was calculated as the sum of all three two way epistatic interactions, with dominance by domin ance having the greate st contribution while additive by dominance was almost zero. Overall, i ncluding the non additive effects i mproves the fitting of the data. A lthough this improvement is small for pedigree models there is a substantial improvement when compared among marker based models (Table 4 2) Given the differences observed in variance component estimations on the models including non additive effects, we studied the sampling correlation among the variance component estimation to evaluate which of the 10 model s was able to better partition the genetic variance (Appendix B ). T he correlation of variance components between additive/dominance with epistasis cannot be estimated under the pedigree models as the estimation of the epistasis variance was z ero ( Appendix B ). The distribution of the eigenvalues of the portion of the correlation matrices with relevance for genetic s and breeding (additive, dominance, epistasis and error) was calculated (Figure 4 1) excluding additive only models. As reference, t he distribution of eigenvalues for a perfect ly orthogonal correlation matrix (identity matrix) with all of them equal to 1 representing the ideal scenario (Figure 4 1a) The distribution of the eigenvalues is narrower for the matr ix of correlation from mod el D G _MM outperforming the D_ped model (Figure 4 1 b), as an example the correlation between additive and dominan ce variance components decrease d from 0.90 with the D_ped to 0.70 with the D G _MM model ( Appendix B ). In general all the marker based models i ncluding epistasis outperform ed their pedigree based counterpart. Models
64 D G #D G _MM and A G #D G _MM showed the best performance (Figure 4 1 c), with correlation values between additive and dominance/epistasis below 0.4 ( Appendix B ). In both cases, pedigree and marker based, the models including more than one epistasis matrix performed worse than simpler models. These eigenvalue distributions are only comparable for matrices of the same dimension. So the distributions cannot be used to compare between sections b with c in Figure 4 1. Given the results above we studied the standard error of the prediction (SEP) for models including dominance by dominance and additive by dominance for pedigree and marker based model. Figure 4 2 shows the SEP pat tern found for the BV and DV for each of the 860 individual clone s. SEP for BVs from the marker based models w as smaller than the pedigree based models i n 99.8% of the cases (Figure 4 2a and c). For DV a clear advantage was observed for the marker over the pedigree based mo dels with almost all SEP more than 40% worse in the pedigree based models (Figure 4 2b,d). If a given model can estimate variance components free of noise (low correlation among effects) the prediction of BV using these estimations should be mo re accurate. Following this assumption we tested with cross validation the additive models (A_ped and A G _MM) and models including dominance by dominance and additive by dominance for both pedigree (D#D_ped and A#D_ped) and marker based (D G #D G _MM and A G #D G _MM) m odels (Table 4 3) W ith a 10 fold cross validation replacing the A matrix (model A_ped) by the A G matrix (model A G _MM) in the additive models increased BV prediction a bility by 4%. However, in the pedigree based models, inclusion of non a dditive effects increa se s the BV prediction ability by 14% in the D#D_ped model and
65 13% in the A#D_ped model Inclusion of non additive effects i n the marker based models (A G #D G _MM and D G #D G _MM) increase BV prediction by 30% compared with the A G _MM and by 36% when compared to A _ped. T he Mean Square Error (MSE) decreased by 50% from the additive models ( A _ped) to the more complex pedigree bas ed models (D#D_ped and A#D_ped) and it further decrease s to approximately 10 12 % of the value observed in the additive models (A_ped and A G _MM) when the marker based models (A G #D G _MM and D G #D G _MM) were used. Furthermore, we calculate d the rank correlation between real ranking using all data in each model and predicted ranking from the 10 fold cross validation. T he correlation of ranking posit ion including all genotypes showed similar values as the correlation between BVs showed above in Table 4 3 ( data n ot shown). However, i n a breeding program it is not only necessary to predict the trend and magnitude of the complete set of selection candida tes but also to accurately identify the top performers Here, we emulated a selection of the top 10% and studied the correlation of the true ranking position, given by the model including all data, and the predicted position in the ranking using the model in a cr oss validation scenario The capacity to predict the top 10% doubled when the A matrix (0.17) was replaced by the A G ma trix (0.34) in the additive models ( A _ped and A G _MM ) and further increase d for the A G #D G _MM model to 0.37 (Table 4 3 ) doubling th e correlations observed in the non additive pedigree based models. The correlation for the model D G #D G _MM was a little lower than the A G _MM model; however still 80% better than the best pedigree model. Discussion As expected, when the A matrix was replace d by the A G matrix in the additive BLUP analysis the heritability increased with the accuracy of the model (Hayes et al.
66 2009) I nclusion of non additive effects in the pedigree based full model decreased the narrow sense heritability by 26 %. This result indicates that ignoring non additive effects overestimated the additive variance, and therefore inflates the narrow sense heritability (Lu et al. 1999; Zuk et al. 2012). In addition, when pedigree based model s include non additive effect s the conclusions do not vary from the general trend that non additive effects are a small fraction of the total genetic variation for trees (Isik et al. 2003; Costa e Silva et al. 2004; Baltunis et al. 2007; Araujo et al. 2012). In contrast, marker based models with additi ve and non additive effects yield a totally different variance partitioning than their counterparts using the pedigree. The additive variance decreased as dominance was added to the model and it further decrease s when dominance plus epistasis were consider ed in the models These models indicate that non additive effects are as important as additive effects and certainly larger than can be predict ed with the pedigree models. Although the models that include non additive effects differed in the partitioning o f the variance components they estimate a common non additive variance component. Changes in the magnitude of variance components have already been observed when the relationship matrix derived from markers is used instead of the pedigree derived relation ship matrix (Habier et al. 2010) Th e values for the model selection criteria (AIC) varied slightly for the best models, D_ped, D#D_ped, A#D_ped, A G #D G _MM and D G #D G _MM and thus no clear advantage of one o ver any other model can be declared. Consequently, w e compared the capacity of the different models to partition the random effects estimates by using the sampling correlation among them. Under perfect orthogonality of genetic effects the sampling correlation among the model effects will be closer to zero and eigenvalues of this
67 correlation matrix close to one (Figure 4 1a) indicating a perfect separation of effects (Hill 2010). In the additive plus dominance and additive plus dominance plus epistasis cases, models derived from molecular markers more effic iently partition ed the genetic effects than their counterpart pedigree based models. The parameterizations of these paired models were identical except for the origin of the relationship matrices (pedigree or marker based ) The poor capacity of pedigree m odels to partition is not surprising as all relationship matric es are derived from the additive relationship matrix derived from the pedigree (Mrode 2005) and so they are strongly correlated (Visscher 2009) The D G #D G _MM and A G #D G _MM models had the weakest correlation s between additive and non additive below 0.4 showing they partitioned effects substantially better than the best value of pedigree based models of 0.89 ( Appendix B ) similar to the value of 0.82 reported by Visscher ( 2009 ) These results supp ort the finding that pedigree derived models cannot separate the additive from non additive effects as their results are comparable to those of additive models (Hill et al. 2008). On the other hand, t he use of the matrix derived from markers has already be en related to a better capacity of separate genetic from environment al effects (Habier et al. 2010) and thu s we conclude that the use of these matrices also increase the capacity to separate additive from non additive genetic effects. We further studied th e ability of a subset of models to predict the additive effect (BV) using a 10 fold cross validation strategy We expected that 1) a better estimate of the additive effect should be more stable in a cross validation scenario 2) i f non additive effects exi st and are significant then models including non additive effects should be able to predict better than additive only models, and 3) the full model that
68 separate s better additive from non additive and environment effects should provide a better vector of BV to be predicted. We found that by replacing the A matrix with the A G matrix in the additive models the prediction ability i ncreases by 4% (Table 4 3 ), as expected for a quantitative trait of these characteristics (Hayes et al. 2009 ). Furthermore, the in clusion of non additive relationship matrices (D G and either D G #D G or A G #D G ) together with A G yi elded a BV predictive ability 36 % larger than pedigree models and 30 % larger than the additive model with the A G matrix which is the traditional GBLUP In addi tion, the mean square error of the last model s (D G #D G _MM and A G #D G _MM) decreased significantly m ore than 8 fold and 4 fold when compared with non additive pedigree and additive marker model s respectively. Moreover, t he smaller SEP s for marker derived mode ls (Figure 4 2) with the complete dataset also support these findings These results indicate that, to increase substantially the accuracy to predict the BV for this trait, replacing the A matrix by the A G matrix is not enough and non additive effects need to be considered Overall, the se result s support the idea of Hill et al. (2008) that if non additive effects exist th ey will be partially captured as additive effects. However, this does not mean that non additive effects do not exist We demonstrate tha t the marker derived model s better separat ed additive from non additive effects and also yield better predicti ons of BV for tree height an important trait in tree breeding W e conclude that the use of relationship matrices derived from markers in a model i ncluding additive and non additive effects had the best performance not only to partition the genetic variances but to improve considerably the breeding value prediction ability in trend, magnitude and top individual selection. Moreover, t his study reveale d that additive and epistatic effects are
69 of similar magnitude for height growth in Pinus taeda, a novel result that should promote new improvement strategies. Finally, u sing markers rather than pedigree derived matrices in linear mixed models with additiv e and non additive effects p rovides a more accurate estimation of the variance components that change our understanding of the genetic control and genetic architecture of a quantitative trait inferred by the pedigree information.
70 Table 4 1 Summary of mod els, effects fitted and relationship matrices used in the study. Model Number Model Effect fitted Relationship matrix used 1 A_ped a A 7 A G _MM a A G 2 D_ped a,d A,D 8 D G _MM a,d A G ,D G 3 A#A_ped a,d,aa A,D,A#A 9 A G #A G _MM a,d,aa A G ,D G ,A G #A G 4 D#D_ped a, d,dd A,D,D#D 10 D G #D G _MM a,d,dd A G ,D G ,D G #D G 5 A#D_ped a,d,ad A,D,AD 11 A G #D G _MM a,d,ad A G ,D G ,A G #D G 6 Full_ped a,d,aa,dd,ad A,D,A#A,D#D,A#D 12 Full_MM a,d,aa,dd,ad A G ,D G ,A G #A G ,D G #D G ,A G #D G
71 Table 4 2. Variance estimation, genetic parameters ( standard errors in parenthesis) and measure of data fitting. A_ped A G _MM D_ped D G _MM A#A_ped A G #A G _MM D#D_ped D G #D G _MM A#D_ped A G #D G _MM Full_ped Full_MM LogL 1299.40 1336.44 1295.37 1311.63 1294.83 1297.60 1293.90 1294.95 1294.38 1294.77 1295 .85 1296.42 Number effects 4 4 6 6 8 8 8 8 8 8 8 9 AIC 2606.80 2680.88 2602.74 2635.26 2605.66 2611.20 2603.80 2605.90 2604.76 2605.54 2607.7 2610.84 Iblk 2512.10 2491.64 2513.88 2491.69 2514.21 2498.05 2513.72 2504.49 2514.05 2503.37 2513.83 2499.48 Additive (Add) 3682.82 4367.48 2599.18 2130.05 2577.58 559.65 2516.89 1327.21 2553.12 1105.90 2258.46 1051.46 Dominance (Dom) 622.84 1452.33 606.84 372.46 636.18 195.77 623.13 204.43 0.00275 197.18 Epistasis Add x Add 0.01 1868.51 883 .27 569.48 Epistasis Dom x Dom 0.00 1231.60 0.00126 957.52 epistasis Add x Dom 0.00 1432.87 0.01 Culture x Add 200.95 138.18 115.88 146.63 0.00 146.03 92.04 80.29 91.83 59.06 112.064 145.25 Culture x Dom 127.51 4.7 6 0.00 16.32 0.00 0.00 0.00 0.00 135.65 18.85 culture x (Add x Add) 282.85 0.00 culture x (Dom x Dom) 213.40 189.52 culture x (Add x Dom) 196.84 214.24 Residual 5129.61 5263.04 5095.98 5198.93 5068.76 5149.97 5054.42 5073.86 5065.71 5075.45 5092.09 5142.39 Total Variance 9013.38 9768.70 8561.38 8932.70 8536.04 8112.94 8512.93 8098.25 8530.64 8091.95 8481.54 8082.12 h 2 SE(h 2 ) 0.409 (0.018) 0.447 (0.021) 0.304 (0.059) 0.239 (0.039) 0.302 (0.058 ) 0.069 (0.050) 0.296 (0.058) 0.164 (0.041) 0.299 (0.058) 0.137 (0.043) 0.266 (0.081) 0.130 (0.059) d 2 SE(d 2 ) na na 0.073 (0.044) 0.163 (0.032) 0.071 (0.043) 0.046 (0.039) 0.075 (0.042) 0.024 (0.039) 0.073 (0.043) 0.025 (0.040) 0.000 (0.000) 0.024 (0.040) i 2 SE(i 2 ) na na na na 0.000 (0.000) 0.230 (0.048) 0.000 (0.000) 0.152 (0.034) 0.000 (0.000) 0.177 (0.039) 0.104 (0.063) 0.189 (0.051) H 2 SE(H 2 ) 0.409 (0.018) 0.447 (0.021) 0.376 (0.023) 0.401 (0.020) 0.373 (0.023) 0.345 (0.021) 0.370 (0.023) 0.340 (0.02 1) 0.372 (0.024) 0.339 (0.021) 0.370 (0.026) 0.343 (0.021)
72 Table 4 3. Predictive abil ity, Mean Square Error (MSE), top 10% ranking correlation (Top10%RankCor) and AIC for selected models. Model Cor(RBV,PBV) MSE(RBV,PBV) Top10%RankCor AIC A_ped 0.640 1 335.800 0.17 2606.80 A G _MM 0.670 1291.800 0.34 2680.88 A#D _ped 0.727 657.258 0.16 2604.76 A G #D G _MM 0.872 108.240 0.37 2605.54 D#D _ped 0.732 638.464 0.18 2603.80 D G #D G MM 0.873 151.199 0.32 2605.90
73 Figure 4 1. Eigenvalue distribution for a perfect orthogonal correlation matrix (a), for models including additive and dominance (b) and for models including additive, dominance and epistasis (c). White box for pedigree and grey for marker derived models.
74 Figure 4 2. Standard error of the prediction (SEP) for pedigree derived matrices model (X axis) against their counterpart using marker derived matrices (Y axis). a) SEP for BV prediction model including A#D interaction. b) SEP for dominance value (DV) prediction model including A#D interaction. c) S EP for BV prediction model including D#D interaction. d) SEP for DV prediction model including D#D interaction.
75 CHAPTER 5 CONCLUSIONS The rapidly decreasing cost of molecular markers (especially SNPs) and the current success of genomic selection in cattle breeding suggest that GS has the potential to become the norm in all breeding programs. In pine breeding, GS has the potential to increase genetic gain by dramatically decreasing the length of the breeding cycle. To apply GS, an important initial investme nt to obtain a dense panel of SNPs markers in a large number of individuals is required. While recently the use of this dense panel of markers has been studied extensively in breeding for prediction of additive effects, this research extended and maximized the use of molecular markers beyond prediction with direct and positive benefit to the breeding program. If GS is planned in a breeding program, we strongly recommend constructing an additive relationship matrix derived from the molecular markers. As show n in this study, this relationship matrix enables detection and correction of pedigree errors (recent and historical) by using the normality property of the different relationship classes. Most types of errors can be corrected by re assigning individuals, parents or families to known pedigree in the records or by creating new parents for individuals that do not match any parent in the records (i.e. result of pollen or seed contamination). Independently of the stage or the kind of error, our results showed t hat correcting the pedigree increases the accuracy of the BLUP BV prediction and dramatically increases the fit of the data. In addition, the corrected pedigree improved the accuracy of GS models in 13 of 15 traits studied, indicating that GS models more e fficiently capture associations between markers and QTLs when the correct pedigree is used to estimate BLUP BV. The use of the normality relationships derived from a large number of SNP
76 markers is envisioned to be complementary to the use of a small number of microsatellites markers for pedigree validation and error correction in the different levels of the breeding cycle (i.e. field trial selections, seed orchards, clonal banks, greenhouse and production/deployment). Following pedigree corrections in the b reeding program, it is highly recommended, that the dense panel of markers should be used to perform GS with at least two analytic methodologies that contrast in the context of marker effect distribution. The methods RR BLUP or GBLUP assume that most genes (markers in the model) will have some effect in the traits being study. This is a suitable assumption when considering an infinitesimal model, where the characters are determined by an infi nite number of unlinked and non epistatic loci, with small effect. In contrast, most Bayesian methods assume that only a portion of the genes will have an effect on the trait. This study shows that trait specific methodologies will be needed, depending on the genetic architecture of the trait. In general, the methods eva luated here ( RR BLUP/RR BLUP B, Bayes A, ) differed only modestly in their predictive ability (defined by the correlation between the direct genetic value and deregressed phenotypes) Not surprisingly, BLUP based metho ds underperformed relative to Bayesian approaches for oligogenic traits as was the case for fusiform rust resistance than RR BLUP in predicting fusiform rust resistance traits, likely reflect ing a simpler genetic a rchitecture, with a few loci of large effect involved in gene for gene resistance interactions In addition to the published models, we developed RR BLUP B, aimed at reducing the number of parameters as an alternative to Bayesian and the traditional RR BL UP approaches For rust disease
77 resistance and wood density traits, RR BLUP B approach performed bett er that traditional RR BLUP, as well as the Bayesian methods. While RR BLUP B may add an additional step to the development of predictive models (i.e. init ial marker selection), it is overall simpler and computationally less expensive than Bayesian approaches. Therefore, it may provide a suitable alternative to the use of BLUP based methods for traits that do not fit an infinitesimal model and are regulated by few major loci. The problem is that the genetic architecture of most traits in breeding programs is not known, thus based on the results of two contrasting GS methods in a cross validation or directly in a validation population will help to elucidate th is. Finally, the molecular markers should be used to study the existence and magnitude of non additive effects on the trait of interest. In this study, we showed that compared with pedigree derived relationship matrices molecular marker derived relationshi p matrices (additive and non additive) in a linear mixed model better partition the genetic variance into additive and non additive components. The result of this study supports the idea of Hill et al. (2008) that if non additive effects exist additive eff ects will capture them Which, does not imply that non additive effects are non existent. We showed that the use of marker derived relationship matrices are able to extract more information from the same phenotypic dataset, due that these matrix better ref lect the real additive and non additive relationship among the individuals. For example height, an important trait in tree breeding, we conclude that the use of relationship matrices derived from markers in a model including additive and non additive effec ts had the best performance not only to partit ion the genetic variances but improv ing considerably the breeding value prediction ability in trend, magnitude and top individual selection. This
78 study revealed that additive and non additive epistatic interact ions effects are of similar magnitude for height in Pinus taeda, a novel result that that can drive new improvement strategies for the species. In addition, u sing this model provides a more accurate estimation of the variance components that change d the vi ew of the genetic control and architecture inferred by the pedigree information. Overall, the results of this study support the idea that molecular markers can be used beyond prediction of breeding values in breeding populations. While the species Pinus ta eda was used as a model here, our recommendations are not species specific and should be considered in animal and plant breeding programs. In summary, is strongly recommended for breeding programs that will be using genomic selection to use the molecular m arkers to: 1) confirm the pedigree and check for errors; 2) study the trait genetic architecture; 3) run at least two genomic selection methodologies that differ in the assumptions of number of genes controlling the trait (e.g. GBLUP, Bayes Cpi) to select the appropriate one for each trait, and; 4) predict non additive effects, given the genetic architecture of the trait. In this way, maximum advantage can be obtained from the molecular markers. Some strategic scenarios should be considered depending on the quantitative pattern with many genes (i.e. markers) controlling the trait, then GS should be considered. Otherwise, if the trait is controlled by major genes (oligogen ic) then traditional marker assisted selection (MAS) should be considered together with GWAS, as chances for gene discovery are higher under this case. While the study of quantitative genetics is mature, the use of molecular markers in breeding is re vital izing the study in this area. A large number of studies have focused
79 on analyzing different aspects of quantitative genetics but there are still several important areas that need further improvement: genetic by environment interaction, genetic architecture of important traits, prediction of non additive effects, strategies of improvement that better exploit the faster cycles times due to GS and addition of expression data to improve prediction models are some of these. Finally, the use of prediction models that incorporate GS with growth modeling and expression data is envisioned as a target to improve the prediction across areas of deployment and thus predict the genotype by environment in addition to genotype performance in pine breeding programs.
80 APPEND IX A PREDICTIVE ABILITY, STANDARD ERRORS AND REGRESSION COEFFICIENTS FOR DIFFERENT GENOMIC SELECTION MODELS OF CHAPTER 2 Table A 1. Predictive ability ( and standard error (SE) of RR BLUP model under two different cross validation methods : 10 fold cross validation and leave one out (L1 Out) Trait Category Trait Methods 10 Fold SE 10 Fold L1 Out SE L1 Out Grow th HT 0.39 0.029 0.38 0.029 Growth HTLC 0.45 0.027 0.46 0.027 Growth BHLC 0.49 0.026 0.49 0.026 Growth DBH 0.46 0.027 0.46 0.027 Development CWAL 0.48 0.029 0.48 0.030 Development CWAC 0.38 0.026 0.40 0.027 Development BD 0.27 0.032 0.27 0.032 Devel opment BA 0.51 0.025 0.52 0.025 Development Rootnum_bin 0.28 0.030 0.28 0.030 Development Rootnum 0.24 0.031 0.24 0.031 Disease resistance Rust_bin 0.29 0.032 0.29 0.033 Disease resistance Rust_gall_vol 0.23 0.033 0.24 0.033 Wood quality StiffnessTree 0.43 0.027 0.43 0.028 Wood quality Lignin 0.17 0.032 0.17 0.032 Wood quality Latewood%4 0.24 0.031 0.25 0.031 Wood quality Density 0.20 0.032 0.21 0.032 Wood quality C5C6 0.26 0.031 0.27 0.031
81 Table A 2 Regression Beta and standard error (SE) of t he RR BLUP model with two different cross validation methods : 10 fold cross validation and leave one out (L1 Out) Trait Category Trait Methods Beta 10 Fold SE 10 Fold Beta L1 Out SE L1 Out Growth HT 1.18 0.10 1.12 0.09 Growth HTLC 1.20 0.08 1. 21 0.08 Growth BHLC 1.11 0.07 1.11 0.07 Growth DBH 1.19 0.08 1.17 0.08 Development CWAL 1.04 0.06 1.03 0.06 Development CWAC 1.10 0.09 1.13 0.09 Development BD 1.23 0.15 1.19 0.15 Development BA 1.13 0.07 1.13 0.06 Development Rootnum_bin 1.36 0.15 1.31 0.15 Development Rootnum 1.51 0.20 1.48 0.19 Disease resistance Rust_bin 1.13 0.13 1.12 0.13 Disease resistance Rust_gall_vol 1.29 0.19 1.23 0.18 Wood quality StiffnessTree 1.12 0.08 1.10 0.08 Wood quality Lignin 1.00 0.19 0.96 0.19 Wood quality Latewood%4 1.01 0.14 1.03 0.13 Wood quality Density 1.26 0.20 1.27 0.20 Wood quality C5C6 1.22 0.15 1.23 0.15
82 Table A 3 Standard error of the prediction models for the different methods tested. Trait Category Trait Methods RR BLUP BLASSO Bayes A B Growth HT 0.029 0.029 0.029 0.029 Growth HTLC 0.027 0.027 0.028 0.028 Growth BHLC 0.026 0.026 0.026 0.026 Growth DBH 0.027 0.027 0.027 0.027 Development CWAL 0.029 0.030 0.030 0.030 Development CWAC 0.026 0.027 0.027 0.027 Development BD 0.0 32 0.032 0.032 0.032 Development BA 0.025 0.025 0.025 0.025 Development Rootnum_bin 0.030 0.030 0.031 0.031 Development Rootnum 0.031 0.031 0.031 0.031 Disease resistance Rust_bin 0.032 0.033 0.031 0.031 Disease resistance Rust_gall_vol 0.033 0.033 0. 033 0.033 Wood quality StiffnessTree 0.027 0.028 0.028 0.028 Wood quality Lignin 0.032 0.032 0.032 0.032 Wood quality Latewood%4 0.031 0.031 0.032 0.031 Wood quality Density 0.032 0.032 0.032 0.032 Wood quality C5C6 0.031 0.031 0.031 0.031
83 Table A 4 Accuracies of genomic selection mo dels in 17 different traits of loblolly p ine. h 2 m represents the Mendelian segregation and was the correction factor used to convert predictive abilities into accuracies Trait Category Trait h 2 m Methods RR BLUP BLAS SO Bayes A Growth HT 0.66 0.48 0.47 0.47 0.47 Growth HTLC 0.53 0.62 0.60 0.60 0.60 Growth BHLC 0.52 0.68 0.68 0.68 0.68 Growth DBH 0.66 0.57 0.57 0.57 0.57 Development CWAL 0.43 0.58 0.55 0.55 0.55 Development CWAC 0.63 0.60 0.58 0.59 0.59 Development BD 0.26 0.53 0.49 0.53 0.53 Development BA 0.5 0 0.72 0.72 0.72 0.72 Development Rootnum_bin 0.5 0 0.40 0.40 0.38 0.40 Development Rootnum 0.43 0.37 0.40 0.38 0.37 Disease resistance Rust_bin 0.21 0.63 0.61 0.74 0.74 Disease resistance Rust_gall_vol 0.18 0.57 0.57 0.66 0.68 Wood quality StiffnessTree 0.37 0.71 0.64 0.69 0.69 Wood quality Lignin 0.11 0.51 0.51 0.51 0.51 Wood quality Latewood%4 0.17 0.58 0.58 0.56 0.58 Wood quality Density 0.09 0.67 0.73 0.77 0.73 Wood quality C5C6 0.14 0.69 0.67 0.67 0.67
84 Table A 5 Regression coefficients estimates of deregressed phenotypes regressed on Direct Genetic Values. Estimates for the model RR BLUP are presented in the Supporting Material Table A 2. Trait BLASSO SE (BLASSO) Bayes A SE (Bayes A) BayesC SE (Bayes C HT 0.97 0.08 0.90 0.08 1.02 0.09 HTLC 0.98 0.07 0.93 0.06 1.00 0.07 BHLC 0.98 0.06 0.98 0.06 1.01 0.06 DBH 0.99 0.07 0.97 0.06 1.02 0.07 CWAL 0.90 0.08 0.87 0.08 0.95 0.08 CWAC 0.91 0.06 0.91 0.06 0.99 0.06 BD 0.97 0.13 0.97 0.12 1.08 0.1 3 BA 0.96 0.06 0.99 0.06 0.99 0.06 Rootnum_bin 1.01 0.11 0.85 0.10 1.04 0.12 Rootnum 1.01 0.13 1.04 0.14 1.05 0.14 Rust_bin 0.88 0.11 1.04 0.10 1.00 0.10 Rust_gall_vol 1.00 0.14 1.04 0.13 1.11 0.13 StiffnessTree 0.83 0.06 1.04 0.08 0.99 0.07 Lignin 1.01 0.20 0.87 0.17 1.11 0.21 Latewood%4 0.93 0.13 0.84 0.12 0.96 0.13 Density 0.95 0.14 0.99 0.14 1.04 0.15 C5C6 0.95 0.12 0.97 0.13 1.01 0.13
85 Table A 6 Predictive abilities of RR BLUP_B when a reduced subset of markers was used compared to the pre dictive abilities of RR BLUP Trait RR BLUP RR BLUP_B Subset length HT 0.38 0.38 4630 HTLC 0.45 0.45 3910 BHLC 0.49 0.50 1380 DBH 0.46 0.46 3800 CWAL 0.38 0.39 820 CWAC 0.48 0.47 590 BD 0.27 0.28 1110 BA 0.51 0.52 1040 Rootnum_bin 0.28 0.28 2550 R ootnum 0.23 0.24 3350 Rust_bin 0.29 0.33 310 Rust_gall_vol 0.23 0.37 100 StiffnessTree 0.43 0.44 1300 Lignin 0.17 0.17 4240 Latewood%4 0.24 0.24 3820 Density 0.20 0.24 240 C5C6 0.25 0.25 4790
86 APPENDIX B SAMPLING CORRELATION MATRICES FOR CHAPTER 4 MODELS Table B 1. Sampling correlation matrix for all models tested. Above diagonal pedigree based and below diagonal marker based models. (A) additive models 1 and 7, (B) additive plus dominance models 2 and 8, (C) additive plus dominance plus additive by additive models 3 and 9, (D) additive plus dominance plus dominance by dominance models 4 and 10, (E) additive plus dominance plus additive by dominance models 5 and 11, and (F) full models 6 and 12. Effect estimated effects are I.block = incomplete blo ck, Add=Additive, Dom=dominance and Cult=silviculture type. A I.Block Add CultxAdd Residual I.Block 1.00 0.00 0.01 0.07 Add 0.00 1.00 0.14 0.08 CultxAdd 0.01 0.08 1.00 0.24 Residual 0.07 0.13 0.19 1.00 B I.Block Add Dom CultxAdd CultxDom Residual I.Block 1.00 0.00 0.00 0.00 0.01 0.07 Add 0.00 1.00 0.90 0.08 0.05 0.04 Dom 0.00 0.70 1.00 0.09 0.15 0.02 CultxAdd 0.00 0.12 0.12 1.00 0.62 0.02 CultxDom 0.01 0.09 0.17 0.69 1.00 0.26 Residual 0.07 0.05 0.02 0.00 0.19 1.00 C I.Block Add Dom AddxAdd CultxAdd CultxDom Cultx(AddxAdd) Residual I.Block 1.00 0.00 0.00 0.07 0.07 0.07 0.01 0.07 Add 0.00 1.00 0.89 0.02 0.02 0.02 0.04 0.02 Dom 0.01 0.19 1.00 0.01 0.01 0.01 0.07 0.01 AddxAdd 0.00 0.55 0.56 1.00 1.00 1.00 0.30 1.00 CultxAdd 0.00 0.11 0.11 0.00 1.00 1.00 0.30 1.00 CultxDom 0.01 0.07 0.16 0.01 0.69 1.00 0.30 1.00 Cultx(AddxAdd) 1.00 0.30 Residual 0.07 0.03 0.03 0.07 0.01 0.19 1.00
87 D I.Block Add Dom DomxDom CultxAdd CultxDom Cultx(DomxDom) Residual I.Block 1.00 0.00 0.00 0.07 0.01 0.07 0.00 0.07 Add 0.00 1.00 0.89 0.01 0.02 0.01 0.05 0.01 Dom 0.00 0.35 1.00 0.01 0.04 0.01 0.07 0.01 DomxDom 0 .00 0.29 0.62 1.00 0.02 1.00 0.31 1.00 CultxAdd 0.00 0.09 0.00 0.10 1.00 0.02 0.48 0.02 CultxDom 0.07 0.00 0.01 0.02 0.04 1.00 0.31 1.00 Cultx(DomxDom) 0.01 0.04 0.00 0.18 0.52 0.31 1.00 0.31 Residual 0.07 0.00 0.01 0.02 0.04 1.00 0. 31 1.00 E I.Block Add Dom AddxDom CultxAdd CultxDom Cultx(AddxDom) Residual I.Block 1.00 0.00 0.00 0.07 0.01 0.07 0.00 0.07 Add 0.00 1.00 0.89 0.02 0.03 0.02 0.02 0.02 Dom 0.00 0.29 1.00 0.01 0.06 0.01 0.10 0.01 AddxDom 0.00 0. 38 0.62 1.00 0.03 1.00 0.30 1.00 CultxAdd 0.00 0.10 0.00 0.11 1.00 0.03 0.54 0.03 CultxDom 0.07 0.00 0.01 0.02 0.08 1.00 0.30 1.00 Cultx(AddxDom) 0.01 0.05 0.00 0.17 0.62 0.31 1.00 0.30 Residual 0.07 0.00 0.01 0.02 0.08 1.00 0.31 1.00 F I.Block Add Dom AddxAdd DomxDom AddxDom CultxAdd CultxDom Residual I.Block 1.00 0.00 0.07 0.00 0.07 0.00 0.01 0.07 Add 0.00 1.00 0.03 0.94 0.03 0.09 0.10 0.03 Dom 0.01 0.29 1.00 0.02 1.00 0.02 0.26 1.00 AddxAdd 0.00 0.68 0.0 2 1.00 0.02 0.11 0.17 0.02 DomxDom 0.00 0.52 0.30 0.90 1.00 0.02 0.26 1.00 AddxDom 0.07 0.00 0.04 0.01 0.04 1.00 CultxAdd 0.00 0.10 0.11 0.00 0.00 0.01 1.00 0.62 0.02 CultxDom 0.01 0.07 0.16 0.00 0.01 0.19 0.69 1.00 0.26 Residua l 0.07 0.00 0.04 0.01 0.04 1.00 0.01 0.19 1.00
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95 BIOGRAPHICAL SKETCH Patricio R. Munoz was born in Santiago, Chile. His parents are Margarita Del Valle and Luis Munoz. He is the 7 th of 8 siblings. He lived h is childhood in Pirque, a town l ocated at the foot of the Andes mountains. He then moved to the south of Chile where he obtained the title of Forestry Engineer from the Univers idad Catolica de Temuco He worked for Forestal Mininco (CMPC Forestal) for about two years as a breeder assista nt and data analyst in the tree improvement program. He then moved to the University of Florida (Gainesville) where he obtained a Master of Science on quantitative genetics at the School of Forestry Resources and Conservation (SFRC). Curio u s on how to bett er integrate traditional breeding with molecular information, he decided to pursue a PhD i n the Plant Molecular and Cellular Biology program (PMCB) at the University of Florida.